网络重建中的接触异质性：评估用于狂犬病传播建模的合成图生成器 机翻

Contact heterogeneity in network reconstruction: evaluating synthetic graph generators for rabies transmission modeling Inez Derkx 1,2* , James Mac Hyman 3 , Fatima Abdelrazak Zakaria 4 , Mahamat Fayiz Abakar 4,5 , Salome D ̈urr 6 , Nakul Chitnis 1,2 1 Swiss Tropical and Public Health Institute, Allschwil, Switzerland 2 University of Basel, Basel, Switzerland 3 Tulane University, New Orleans, Louisiana, United States of America 4 Institut de Recherche en Elevage pour le D ́eveloppement (IRED), N’Djamena, Chad 5 Institut National de Sant ́e Publique du Tchad (INSAPT), N’Djamena, Chad 6 Veterinary Public Health Institute, Vetsuisse Faculty, University of Bern, Bern, Switzerland * inez.derkx@swisstph.ch Abstract Canine rabies remains endemic across much of Africa and Asia, causing approximately 59,000 global deaths yearly. Network-based models that reconstruct contact patterns are central to predicting canine rabies transmission and to designing targeted interventions, but the choice of network generator algorithm may alter network structure and outbreak predictions. We therefore compared five network generators using five empirical free-roaming dog contact networks from Chad, Indonesia, and Guatemala in network topology and outbreak dynamics under susceptible-exposed-infectious-removed (SEIR) and susceptible-infectious-susceptible (SIS) transmission across a range of infectious-period lengths. We found that the degree-corrected stochastic block model (DCSBM) most consistently reproduces both empirical topology and outbreak dynamics, achieving a Mahalanobis distance of 17.6 to the empirical Chad network compared to a range of October 12, 20261/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

21.0 to 220.7 across the other generators and yielding similar results for the other four locations. Moreover, the SIS and SEIR outbreak dynamics reveal that the DCSBM overall best reproduces the simulated empirical outbreak dynamics, but that the consequences of generator choice are not uniform: network reconstruction matters most precisely for short-infectious-window pathogens like canine rabies and progressively less for long-infectious-window pathogens. By an infectious window of nine days, the outbreak dynamics across four of five generators converge to within two percentage points of the empirical reference, even when their underlying topologies differ substantially. This pathogen-dependent sensitivity offers a principled criterion for when generator selection is consequential and when it is not. This work reiterates the importance of both degree heterogeneity and community structure for faithful contact-network reconstruction in canine rabies modeling, particularly for short-window infectious diseases where contact heterogeneity drives transmission. For longer-window pathogens, simpler generators are likely adequate. Author summary Canine rabies causes around 59,000 deaths worldwide each year, and its spread largely depends on the contact networks domestic dogs form with each other. In these networks, some dogs have far more contacts than others, and this heterogeneous structure shapes how diseases like rabies are spread through a population. These structures can be reconstructed using different models, though the choice of model impacts how well it can reconstruct an observed contact network. Here, we therefore compare five synthetic network models against real contact data collected from dogs in Chad, Indonesia, and Guatemala. We evaluate both the structure of the networks they generate and how well they reproduce outbreak dynamics, comparing the outbreaks resulting from the networks generated by each model to outbreaks simulated on the observed networks themselves. One model, the degree-corrected stochastic block model, best reproduces the observed contact structures across locations and comes closest to matching outbreak simulations based on the observed network. We also find that model choice matters more when pathogens have short infectious periods: the models diverge more in their outbreak outcomes under short infectious windows and all but one become October 12, 20262/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

more similar when infectious periods are longer. October 12, 20263/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

Introduction1 Contact patterns play a vital role in the spread of infectious diseases [1–3]. While compartmental population2 models of disease spread traditionally assume homogeneity in contact patterns [4], population contact3 structures are generally heterogeneous and impact the duration, size and dynamics of epidemic4 outbreaks [5–10].5 Incorporating heterogeneous contact structures in disease models has highlighted how the social positions6 of individuals and their clustered interactions can alter disease transmission patterns and help in designing7 targeted intervention strategies [3, 11–14]. For instance, individuals with a greater number of contacts (degree8 centrality) tend to be disproportionately exposed to pathogens and therefore pose a high risk to epidemic 9 outbreaks; and degree heterogeneity can substantially lower or even remove the conventional epidemic10 threshold of mean-field epidemiological models [13, 14]. In networks with strong community structure,11 targeting individuals who function as bridges between communities (betweenness centrality) has been shown12 to be an effective intervention strategy [15–18]. In addition to individual-scale heterogeneity, network13 clustering (global clustering coefficient) can also profoundly impact epidemic dynamics, with increased14 clustering leading to more local spread but simultaneously a reduction in epidemic growth rate [19–21].15 Although capturing the heterogeneity of population contact structures is therefore required to model16 disease dynamics, this effort also relies on the accuracy of empirical proximity-based networks and their17 ability to represent pathogen transmission opportunities. This requirement is best met for pathogens18 transmitted exclusively via direct contact or close proximity, such as rabies [22, 23]. Canine rabies is a19 zoonotic disease responsible for approximately 59,000 yearly human deaths globally and is still endemic in20 many countries in Africa and Asia [24, 25]. Different network-based approaches have successfully used contact21 structures to model canine rabies transmission, for instance linking its persistence to social disruptions22 caused by rabies-induced behavioral changes [26] and providing support for network centrality-based targeted23 vaccinations in domestic dog populations [3].24 In the latter study, Laager et al. [3] generated synthetic population networks from domestic dog proximity25 data using a spatially explicit network construction algorithm, with model outcomes matching city-wide26 rabies outbreak data from N’Djamena, Chad. Even though empirical degree distribution guided edge27 formation, other sources of heterogeneity were not considered. Given the impact of degree and community28 structure on epidemic dynamics, it is likely crucial that network generator algorithms encapsulate not only29 local (individual-level), but also global (network-level) contact variation [27, 28]. However, it remains unclear30 whether incorporating different or additional sources of heterogeneity in network reconstruction improves31 October 12, 20264/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

rabies transmission prediction.32 Numerous generative models exist that could address this gap and have been used to reconstruct33 empirical networks, and which can optimize both local and global network characteristics [29–33]. These34 include random graph generators without population structure (e.g., Erd ̋os–R ́enyi graphs [34]), scale-free35 network models (e.g., Barab ́asi–Albert model [35]), models optimized to produce specific local or global36 structural properties such as degree distribution (e.g., Chung–Lu model [36]), community structure (e.g.,37 stochastic block model and variations thereof [37]), or clustering through triadic closure (e.g., clustered38 random-graph model [38, 39]). The successful application of these models highlights their potential as39 synthetic network generators for disease modeling. Yet, systematic comparisons of how different models,40 including the previously used model of Laager et al. [3], capture empirical contact heterogeneity and the41 consequences thereof for rabies modeling are still lacking.42 This paper therefore assesses the role of contact heterogeneity in network reconstruction for rabies43 modeling and asks a more general question: when does the choice of network generator actually matter for44 outbreak prediction, and when does it not? We compare five network generator algorithms against an45 empirical contact network of dogs residing in N’Djamena, Chad, and across four additional locations in46 Indonesia and Guatemala. Specifically, we examine a) how the synthetic networks compare in network47 topology to their empirical references, b) how the variation in graph heterogeneity impacts disease48 transmission in outbreak simulations of an SEIR rabies model and an SIS model (e.g., common cold) for49 comparison, and c) whether these findings generalize when applied to other variably sized empirical contact50 networks. This work extends the rabies-modeling study of Laager et al. [3], which evaluated a single spatially51 explicit network construction algorithm (SENCA), by placing four additional generator families alongside it52 and testing whether their alternative encoding of heterogeneity improves transmission-prediction fidelity. It53 also builds on recent comparative work on stochastic block models for empirical contact networks [32] by54 pairing topology comparison with full SEIR and SIS outbreak simulations across multiple infectious-period55 regimes, rather than comparing topology alone.56 While numerous alternative models could be explored for this purpose, we limit our comparison to five57 models which in combination examine the relative importance of three axes of structural heterogeneity:58 degree-distribution, community structure, and explicit triadic-closure (clustering) targeting, allowing us to59 assess the incremental contribution of each structural feature to network reconstruction and simulated60 transmission. As previously stated, these three axes have distinct epidemiological implications, including61 individual contribution to acquisition and transmission of infection (degree), extent of localization versus62 universal spreading (community structure), and capturing contact redundancy along with determining63 October 12, 20265/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

infection propagation speed (clustering).64 The models therefore include the SENCA, as introduced above, which is optimized to fit an empirical65 degree distribution [3], a stochastic block model (SBM) which aims to reconstruct empirical community66 structure [37], a degree-corrected stochastic block model (DCSBM) which fits both degree heterogeneity and67 community structure [40], a Newman clustered random-graph generator (NCRG) which additionally targets68 empirical levels of triadic closure [39], and an Erd ̋os–R ́enyi model (ERM) with random contact structure [34]69 as a control. For the remainder of the article, we also refer to these five network generators as ‘graph types’.70 Materials and methods71 Free-roaming dog proximity networks72 We built an empirical contact network from interactions between free-roaming domestic dogs in an urban73 area covering approximately 1 km 2 in N’Djamena, Chad. These data were collected in 2016 using tailor-made74 geo-located contact sensors attached to dog collars over the span of approximately 3.5 days. Rather than75 attempting to sample a single fully connected network, as many dogs as possible inhabiting the covered study76 area were sampled. The resulting network may therefore include isolated individuals or sub-groups. While77 GPS coordinates of the home locations of all dogs as well as individual GPS locations were also collected,78 these were not included in contact or network formation. We used data collected in district six of the city to79 create an undirected, unweighted simple contact network of 235 dogs. In this network, two nodes (dogs) are80 connected by an edge (contact) if they were observed in close proximity at least once during the study period.81 This network is referred to as ‘empirical network’ throughout the remainder of the manuscript. Further82 information about the data collection can be found in detail in Laager et al. [3].83 In addition to this empirical network, we examined previously published contact data of free-roaming84 domestic dogs in Indonesia and Guatemala collected in 2018 for further comparison [41]. The study areas85 include two rural sites in Guatemala: La Romana and Sabaneta; and one rural and one semi-urban site in86 Indonesia: Hepang and Habi, respectively. Data collection followed a similar protocol compared to the 201687 study in Chad, including how the area of the study sites was selected, how the dogs were sampled, and how88 contacts were established using geo-located sensors. Further detailed descriptions of the study sites and data89 collection can be found in Warembourg et al. [41]. While these networks are also empirical contact networks,90 we refer to them throughout the manuscript by their location names instead (e.g., the Sabaneta network).91 October 12, 20266/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

Network generator algorithms92 We generated networks using five models representing distinct combinations of degree-distribution93 heterogeneity, community structure, and clustering (Table 1). Detailed specifications of each generator are94 provided below.95 First, we tested a previously published spatially explicit network construction algorithm (SENCA), which96 was designed to model rabies outbreak dynamics by generating a similar degree distribution to the empirical97 network it is based on [3]. In short, this algorithm requires a pre-defined number of nodes, assigns them98 coordinates using random sampling, and implements a two-step process starting with spatial edge99 construction followed by preferential edge attachment optimized to minimize the Kolmogorov-Smirnov100 distance between the generated and empirical degree distributions. This algorithm has been successfully used101 to model rabies outbreaks, with results matching real-world outbreak dynamics and vaccination coverage in102 N’Djamena, Chad. A more detailed breakdown of the algorithm and its previous implementations can be103 found in Laager et al. [3].104 Table 1. Comparison of the five graph generators and their structural properties.Columns give the network type, how links between nodes are created, and whether the degree distribution, community structure, and explicit triadic-closure (clustering) targeting are modeled. The fifth, sixth and seventh columns summarize each generator’s structural signature. Graph type Abbrev. Network type Edge creation Degree dist. Community structure Cluster. target Source SpatialSENCAAssortative mixing Spatial and preferential attachment of links Heterog.NoNoLaager et al. [3] Stochastic Block SBMAssortative mixing Based on community membership Homog. (within comm.) YesNoHolland et al. [37] Degree- Corrected Stochastic Block DCSBMAssortative mixing Community membership and node degree Heterog.YesNoKarrer & Newman [40] Newman Clustered Random Graph NCRGTriangleaugmented configuration Single-edge and triangle-edge stubs matched to empirical degree and clustering Heterog.No (implicit)Yes (explicit) Newman [39] Erd ̋os–R ́enyiERMRandomRandomHomog.NoNoErd ̋os & R ́enyi [34] Furthermore, we explored the performance of a stochastic block model (SBM) [37] and one of its105 extensions: the degree-corrected stochastic block model (DCSBM) [40]. The SBM is built on the premise that106 the probability of an edge between two nodes relies solely on the communities (‘blocks’) to which those nodes107 belong and hence assumes homogeneity between nodes within the same communities. In empirical networks,108 these communities could for instance reflect geographical neighborhood clusters or dog packs that more109 frequently interact, though they are treated as latent properties of the network in this study. The DCSBM110 introduces a degree parameterψthat represents the propensity of nodes to form edges independent of the111 October 12, 20267/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

community to which they belong. It shows the ratio of node degree to its group’s expected degree, hence112 removing within-community node homogeneity [42]. This allows for examination of node-level variability in113 contacts, for instance because some dogs roam further than others and therefore have more contacts, which114 was highlighted as an important factor in rabies transmission in previous work [3]. While the SBM thus115 introduces heterogeneity through community structure, the DCSBM additionally models node degree.116 For both block models, the optimal number of communitiesKis estimated from the empirical adjacency117 matrix A by asymptotic likelihood ratio [43]. Nodes are then allocated to one ofKcommunities through118 regularized spherical spectral partitioning (RSSP). RSSP is a community detection algorithm that applies119 regularization to either the adjacency matrix (if SBM) or the Laplacian matrix (if DCSBM) by adding a120 constant to each element in these matrices, after which clustering is performed on the spherical coordinates121 that are assigned to each node [44, 45]. The resulting community (block) labelsgand the estimated block122 connection probability matrixBare subsequently used to generate the synthetic graph for the SBM, where123 the probabilityP ij of an edge between nodesiandjisB g i g j . The DCSBM instead uses the estimated124 probability matrix ˆ P, calculated usingB,g, andψ, to generate a graph in whichP ij =ψ i ψ j B g i g j . The125 process of selecting and assigningKas well as estimatingB,ψand ˆ Pis performed using the R package126 randnet(v1.0) and all graphs are generated usingigraph(v2.2.2).127 We additionally implemented a Newman clustered random-graph generator (NCRG) following128 Newman [39]. This generator extends a configuration model, which preserves the empirical degree sequence129 while otherwise randomizing all connections, to incorporate triangle structure. The NCRG therefore 130 explicitly targets triadic-closure, a feature which none of the other generators provide, while otherwise 131 treating community structure as an emergent consequence of the rewired topology rather than a tunable132 input. Graph construction relies on a joint degree sequence in which each nodeiis assigned two distinct stub133 (half-edge) counts:s i independent-edge stubs andt i triangle stubs, wheret i reflects the number of triangles134 node i participates in within the empirical network. The joint degree sequence is extracted from a network135 by counting per-node triangle participations to obtaint i , with independent-edge stubs computed as136 s i =k i −2t i , wherek i is the total degree of nodei. Here, the factor of two reflects that each triangle137 contributes two edges to a node’s degree. Triangle stubs are then grouped into triplets by random shuffling138 and matched to form triangles, while independent-edge stubs are paired by random perfect matching,139 following the procedure described by Newman [39]. Because edges can participate in multiple triangles140 simultaneously, the NCRG’s assumption of edge-disjoint triangles may not always hold. In such cases, any141 resulting negatives i values are automatically clamped to zero. The resulting generated graph is simplified by142 removing self-loops and multi-edges. We translated therandomclustergraph function of theNetworkX143 October 12, 20268/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

Python package (v3.6.1) to R for implementation of this model.144 Lastly, we used an Erd ̋os–R ́enyi graph model (ERM) as a baseline to test how the empirical network and145 synthetic heterogeneous networks compare to a random network structure [34]. The R packageigraph146 (v2.2.2) was used to implement this model by randomly drawing a predefined number of edges between a147 predefined number of nodes, which were both set equal to the number of empirical nodes and edges. As a148 result, the average degree and graph density are identical to the empirical network’s degree and density.149 Network construction and preprocessing150 Given that each of the five network generator algorithms is stochastic, we generated multiple graphs per151 graph type. Each algorithm was run 100, 1000, 2000 and 5000 times with different seeds. Five replicates per152 seed were generated and confirmed to be identical, after which we selected one graph per seed for analyses.153 For each resulting graph, we calculated six measures: mean, median, and maximum degree, mean154 betweenness, global clustering (transitivity) and network density. These were used to examine how the155 different graph types and network parameters respond to increasing sampling effort (S1 Fig). The empirical156 graph was included for comparison, but remained consistent across seeds by definition. We employed the157 Mahalanobis distance metric to examine which graph type showed most similarity to the empirical network158 across all six measures.159 From these six measures, we selected mean degree and mean betweenness to formally examine stochastic160 convergence across increasingly larger sampling sizes using a running mean with 95% confidence intervals (S2161 Fig). The running mean captures how the cumulative (moving) average of these two parameters changes as162 the number of seeds increases [46]. Convergence was further assessed via the standard error, the stepwise163 mean drift (the change in mean between successive sample sizes, e.g. 100 to 1000), and the precision gain164 obtained at each step, reflecting the reduction in the standard error (S1 Table). Based on these convergence165 metrics, all 5000 graphs per graph type were used for downstream analyses. Each of the five network166 generators — DCSBM, ERM, NCRG, SBM, SENCA — was therefore run 5000 times, resulting in an equal167 number of stochastic networks. The resulting distributions of mean betweenness, global clustering, network168 density, and average, median, and maximum degree were subsequently compared to the empirical network.169 Rather than running disease models on a single graph or all 5000 graphs per graph generator, we selected170 100 graphs per graph type that best represented the average degree distribution to prevent stochastic graph171 attributes from skewing modeling outcomes. To do so, we first compared all complete degree distributions of172 each graph type and computed the Kolmogorov-Smirnov distance to the empirical degree distribution (S3 173 Fig). We then summarized each graph type’s degree distribution by six statistics computed across all 5000174 October 12, 20269/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

graphs of that type: the minimum, 25th percentile, mean, median, 75th percentile, and maximum degree175 (Table 2). Each individual graph was scored by how closely its own six statistics matched the per-generator176 averages. This yielded six per-statistic scores from 1 (best match) to 5000 (worst match), which were 177 summed into a single ranking score for each graph. Graphs with lower overall ranking scores were thereby178 closer to the average degree distribution for their generator type. The 100 lowest-scoring graphs per graph179 type were retained on the basis that they should best represent the average degree distribution and would180 therefore produce disease simulations characteristic for that graph type.181 Table 2. Degree summary statistics for each graph type averaged over 5000 graphs.For each graph per graph type, the minimum, 25th percentile, median, mean, 75th percentile, and maximum are calculated. These are then summarized by mean over all 5000 graphs (i.e., the minimum represents the average minimum degree for a specific graph type). Model TypeMin25thMedianMean75thMax DCSBM0.0065.72310.96513.95518.82054.463 ERM5.55712.10614.80114.80017.09426.102 NCRG1.00016.25647.08955.61981.491170.138 SBM1.1949.37514.33614.80219.80733.356 SENCA0.0003.17711.63215.39525.92257.426 Empirical1.0006.00011.00014.80019.00064.000 Disease transmission models182 Rabies transmission was simulated using an individual-based discrete stochastic183 susceptible-exposed-infectious-removed (SEIR) model, adapted from previously published models [3, 25]. The184 compartmental structure follows the standard susceptible-exposed-infectious-removed framework [2, 47]. The185 inclusion of exposed and removed compartments, combined with a declining susceptible population over time,186 is expected to slow disease progression and amplify the influence of heterogeneous contact structures. We187 additionally implemented a susceptible-infectious-susceptible (SIS) model, typically used to model for188 instance the common cold, as a comparative model in which individuals return directly to the susceptible189 pool upon recovery, thereby sustaining a larger susceptible population throughout the simulation. This190 allows assessment of how each graph type affects the overall susceptible population across varying infection191 periods and transmission rates representative of variation in SIS-infectious diseases. Model equations for the192 SEIR (Eq 1) and the SIS formulations (Eq 2) are given below; schematic representations, state variables and193 parameter descriptions are provided in the supplementary material (S4 Fig, S2 Table and S3 Table).194 October 12, 202610/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

dS dt =−βSI(1a) dE dt = βSI − 1 δ E(1b) dI dt = 1 δ E− 1 γ I(1c) dR dt = 1 γ I(1d) 195 dS dt =−βSI + 1 γ I(2a) dI dt = βSI − 1 γ I(2b) The SIS model simulation starts with a single infectious nodei, randomly selected from the total set of196 verticesVof the networkG(V,E) withEedges, such thatV I (0) ={i}andI(0) = 1. The total number of197 infectious individuals at any time is represented byI(t) andV I (t) shows the set of vertices in the network198 that are infectious at timet. At each time step, the set of neighborsN(V I ) ofV I (t) is identified, where the199 collective neighborhood ofV I (t) is defined as the union of individual neighborhoods,N(V I ) = S i∈V I (t) N(i)200 and is bound by the total population size (|N(V I )|≤|V|) in which|·|denotes the number of nodes in the201 enclosed set. For eachi, the size of its individual neighborhoodN(i) is dictated by its degreek i , where202 k i ≤|V|−1. The state transition from susceptible to infectious is governed by a Bernoulli trial, which203 determines which susceptible neighborsN S (i) =N(i)∩V S (t) will become infected, whereV S (t) is the set of204 vertices that are susceptible at timet.205 Specifically, each susceptible neighborj S ∈ N S (i) moves to the infectious state ifβ≥r, wherer∈[0,1] is206 a pseudo-randomly generated number andβ∈[0.01,0.2] is the transmission rate. The duration in days207 which the individual remains infected is sampled from a Poisson distribution with meanλequal to the208 recovery periodγ, such thatγ i represents the infectious period of nodei, and has a minimum duration of 1209 day. We evaluate the model’s sensitivity across a range ofγ∈[3,9] days. Individuals immediately return to210 the susceptible state when they are no longer infectious. The outbreak ends a) when there are no longer any211 individuals in the infectious class (I(t) = 0) or b) when the outbreak has reached its time limit att= 1000.212 The SEIR model follows the same process: the simulation starts withV I (0) ={i}andI(0) = 1, and a213 Bernoulli trial in whichP infection =β≥rdetermines which ofi’s susceptible neighborsN S (i) will be214 October 12, 202611/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

infected and therefore move to the exposed state, after which they become infectious.E(t) andI(t) detail215 the total number of exposed and infectious individuals at timetrespectively. The duration in days during216 which individuals remain exposed and subsequently infectious are sampled from Poisson distributions with217 mean (δ= 30) for exposed individuals and mean (γ= 2) for infectious individuals, such thatδ i andγ i 218 represent the duration of the latent and infectious periods respectively for individuali. Once no longer219 infectious, individuals enter the removed state and exit the simulation, such thatR(t) contains the total220 number of removed individuals at timet. The outbreak ends a) when there are no longer any individuals in221 the exposed and infectious class (I(t) +E(t) = 0), which may be a result of a failure to infect other nodes, a222 lack of susceptible neighbors (N S (i) =∅), or a combination of those two conditions, or b) when the outbreak223 has reached its time limit att= 1000.224 In the SEIR model, the average incubation period of 30 days was based on estimates reported in the225 literature on canine rabies. However, these vary widely across studies: while some report incubation periods226 as low as 14 days [48] and an average of approximately 18.6 days across mesocarnivorous reservoir hosts in a227 recent meta-analysis [49], others report higher values such as an average of 27.30 days during the 1948–1954228 canine rabies epidemic in Tokyo [50], 21–60 days depending on rabies strain [51], and periods of up to 125229 days [52]. We therefore opted for an average of 30 days modeled as a Poisson distribution, which has a230 standard deviation of∼5.5 days and therefore captures most of the reported rabies incubation variation.231 While it excludes the extreme tail of incubation periods that has been recorded in a small minority of232 cases [52], this omission is unlikely to alter the comparative findings across generators reported here. The233 infectious period has a mean of two days because we assume that a symptomatic individual will be easily234 recognized as infected with rabies and hence killed as a result of cultural norms and practices before dying235 naturally from the disease. This assumption has been supported and successfully adopted in previous236 research [3, 53]. The SEIR infectious period was therefore held at this empirically established value, and237 γ -sensitivity was probed using the SIS model rather than by varyingγin the SEIR model, since longer SEIR238 infectious periods would no longer correspond to the majority of empirical scenarios.239 We examined outbreak prevalence by calculating the average and peak number of daily active cases240 (E(t) +I(t)) in each outbreak. In these outbreaks, the total number of infections or cumulative incidence241 (CI) was calculated as the sum of all unique infections throughout the entire outbreak duration. We242 additionally calculated the final outbreak size as the total fraction of removed individuals at the last day of243 each outbreak in the SEIR model. Outbreak duration was defined as the point at which the outbreak ceased244 due to exhaustion of the infectious and exposed classes or where the maximum time limit was reached. 245 We categorized outbreaks as minor or major based on the distribution of final outbreak sizes from SEIR246 October 12, 202612/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

simulations, using a kernel density estimate (f(x)) with a narrow bandwidth (h= 0.3) to preserve sensitivity247 to local features. The choice ofh= 0.3 balances sensitivity to bimodality against smoothing of within-mode248 noise. Sensitivity analyses indicated that the distinction between minor and major outbreaks was robust to249 bandwidth adjustment: 98.7% of simulations retained the same classification across the full range of250 h∈[0.1,0.5]. Differences were concentrated among simulations with very low transmission (β= 0.01), with251 ≥ 99.97% of simulations remaining stable at all other Graph-βcombinations. The classifications obtained252 withh= 0.2–0.3 were identical, supporting the use ofh= 0.3 for the main analysis. A point was considered253 a peak if its height exceeded that of its two neighboring points and was at least 2% of the maximum density254 height. We calculated a dynamic threshold as the minimum value between the first and last significant local255 maxima, such that ˆτ= arg min x∈[p 1 ,p L ] f(x), wherep 1 andp L denote the first and last peaks exceeding 2%256 of the maximum density height. This threshold was then used to categorize outbreaks as major or minor,257 and we summarized the mean and standard deviation of final outbreak size and outbreak duration for both258 categories.259 Simulations260 We tested two parameter sampling approaches for the simulations: factorial and random sampling. Factorial261 sampling was initially used to thoroughly explore the entire parameter space, and its output was compared 262 against that of random sampling to assess whether the latter could sufficiently cover the parameter space.263 Both approaches were used to run the disease transmission models for the empirical network and the264 synthetic graphs. For the factorial sampling approach, the design yielded a parameter grid of265 5 (graph types)×100 (graphs per graph type)×39 (β)×{1 or 7}(γ)×1000 (seeds), totaling 19,500,000266 and 136,500,000 simulations for the SEIR and SIS models respectively (Table 3). The empirical graph was267 sampled with 3,900,000 and 27,300,000 parameter combinations respectively with unique seeds268 (1×39 (β)×{1or7}γ×1000×100), the latter for the 100 graphs to ensure equal sampling of theβandγ269 parameters (Table 3). Note thatδ, fixed at a single value in the SEIR model, does not contribute additional270 combinations.271 While this approach is rigorous, it is time- and memory intensive, particularly for larger graphs with272 higher edge density. As a more efficient alternative, we set the total number of outbreaks per graph type at273 500,000 for the SEIR model and 1,000,000 for the SIS model, given its larger number of potential parameter274 combinations, and randomly sampled a number of γandβparameter configurations equal to the total275 outbreak number (Table 3). Each row of this parameter grid was then assigned a unique random seed. For276 synthetic graphs, rows were also assigned a random graph index between 1 and 100. A single ‘master’ seed277 October 12, 202613/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

(s = 100) was set prior to sampling to ensure reproducibility. Only outbreaks with at least one secondary278 infected individual were used for all summary statistics and visualizations, with the exception of the279 calculation of a threshold to distinguish between major and minor outbreaks in which outbreak simulations280 without a secondary infection were included.281 Table 3. Parameter combinations and sampling design for SEIR and SIS models.Numerical values forβ,γ, andδrepresent the number of discrete levels (steps) used in the grid rather than the specific parameter values or ranges (e.g.,δ= 1 indicates a single value fixed at 30 days). For the factorial design, the total simulation count is the product of all parameter levels and repetitions. For the random sampling design, parameters are sampled independently for each outbreak. In the synthetic network scenarios, the total simulation volume is distributed evenly across the five graph types. Notably, there is a substantial difference in scale between the factorial and random sampling totals: factorial sampling produces orders of magnitude more simulations because every parameter combination is exhaustively crossed, while random sampling concentrates compute on a unique-seed-per-outbreak design. ApproachModelTypeIndex βγ δRepsSeedsTotal Simulations Factorial SEIR Syn.5003911 1,000 Unique19,500,000 Emp.1003911 1,000 Unique3,900,000 SIS Syn.500397– 1,000 Unique136,500,000 Emp.100397– 1,000 Unique27,300,000 Random SEIR Syn.Rnd. Rnd.––1Unique2,500,000 Emp.1Rnd.––1Unique500,000 SIS Syn.Rnd. Rnd. Rnd. –1Unique5,000,000 Emp.1Rnd. Rnd. –1Unique1,000,000 ‘Rnd.’ indicates parameters sampled randomly from their respective distributions for each outbreak. ‘Unique’ seeds indicate that each simulation replicate was assigned a distinct random seed (s). Comparison of both approaches confirmed that random sampling sufficiently explored the parameter282 space and reproduced the patterns observed under the factorial approach. This approach was therefore used283 for all subsequent analyses reported in this manuscript and factorial sampling output is provided in S5284 Fig–S7 Fig. All simulations were performed in R and were parallelized using the packagefurrr(v0.3.1).285 Results286 Network topology characterization287 The five graph types produced distinct ensembles of stochastic networks (Fig 1), with variation in their288 distributions of network properties shown in Fig 2 (and S4 Table). Overall, graph types differ the least in289 their distributions of network density and mean degree, potentially because these two measures are not290 directly linked to network heterogeneity: edge density is only an indicator of mean graph connectedness. The291 log-normal shape of most empirical degree distributions results in mean degree being a poor indicator of292 October 12, 202614/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

heterogeneity.293 Fig 1. Example graph visualizations.A) DCSBM, B) Empirical network, C) ERM, D) NCRG, E) SBM, and F) SENCA. For each synthetic network, the graph whose degree distribution best fits the average degree summary statistics for that graph type is visualized in identical layout (see Methods). Nodes are sized as the square root of the node’s degree rescaled to a range between 0 and 10. The NCRG — which explicitly models triadic closure — has both a substantially higher mean degree294 (μ= 55.62) and edge density (μ= 0.24) compared to all other graph types and the empirical graph. This is295 likely because edges in the empirical network are often part of multiple triangles, which leads to a higher296 edge count and therefore also degree in the network reconstruction using the NCRG. The non-clustered297 random graph (ERM) generates a mean degree and network density identical to the empirical graph298 (μ degree = 14.80 andμ density = 0.06, respectively) as a result of its construction method. Of the remaining299 graph types, the SBM yields a mean degree (μ degree = 14.80) and network density (μ density = 0.06) most300 similar to the empirical graph in comparison to the other graph types. The SENCA produces most variation301 in these two measures (μ degree = 15.39 andμ density = 0.07 respectively), which is a pattern that is visible in302 its distributions of maximum and median degree as well (Fig 2). This is likely because it relies more heavily303 on stochastic sampling compared to the other generators, leading to more variation in its output graphs. The304 DCSBM produces similar mean edge density (μ density = 0.06) but lower mean degree (μ degree = 13.95) to 305 the empirical graph and SBM. However, it fits closer to the empirical degree distribution’s tail: by better306 capturing the higher prevalence of low-degree nodes (below the 25th percentile), it more faithfully reproduces307 heterogeneity at the cost of a lower overall mean (Fig 3 and Table 2).308 Fig 2. Network parameter distributions.Distributions of six network parameters — network density, global clustering, mean betweenness, mean degree, median degree, and maximum degree — over 5000 graph iterations of each graph type as well as their observed values in the empirical network. The six measures fall into two informative groups: density, mean degree, and median degree discriminate weakly among the generators because they are largely constrained by construction; global clustering, mean betweenness, and maximum degree discriminate strongly because they capture heterogeneity that only generators with explicit structural assumptions can reproduce. In measures more indicative of heterogeneity, such as global clustering and mean betweenness, the graph309 types show more distinct variation in their distributions and deviate more clearly from the empirical network.310 With the exception of the NCRG, none of the graph types are able to match the empirical network’s311 relatively high clustering coefficient of 0.40. The empirical value as well as the NCRG’s higher clustering312 coefficient (μ clust = 0.54) support the idea that an individual’s neighbors are likely to be connected, leading313 to high clustering via triadic closure in empirical networks and the Newman clustered random graphs [54]. 314 The DCSBM yields the second highest clustering coefficients (μ clust = 0.29), which lies closest to the 315 October 12, 202615/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

empirical value when compared to all other graph types, followed by the SBM (μ clust = 0.20) and the 316 SENCA (μ clust = 0.18). The higher value in the DCSBM compared to the SBM is likely a result of the 317 heterogeneity in not only community membership, like the SBM, but also node connectivity, potentially 318 leading to further clustering within and beyond communities. As expected, the mean clustering coefficient is319 lowest in the ERM (μ clust = 0.06), where triadic closure is comparatively rare [54].320 No generator successfully reproduces the empirical mean betweenness of 215.1: it is highest in the two321 stochastic block models (μ betw = 190.7 andμ betw = 183.1 in the SBM and DCSBM respectively), followed by322 the ERM (μ betw = 152.7), the SENCA (μ betw = 102.6) and lastly the NCRG (μ betw = 92.1). The modeled323 community-structure in the DCSBM and SBM likely leads to the presence of scarce cross-community links324 which act as bridges between clusters and therefore strongly increase mean network betweenness (S8 Fig). In325 contrast, connections in the ERM are entirely independent and the shortest path between any two nodes can326 route through a large variety of alternative paths, keeping the mean and maximum betweenness centrality327 low (S8 Fig). Lower mean betweenness in the SENCA may be explained by the presence of many isolated328 individuals, whose low betweenness values negatively impact the network’s mean betweenness (Fig 1F). In329 the NCRG, the high density of edge triangles likely translates to a large number of alternative shortest paths330 and therefore lower betweenness scores for individual nodes.331 The last two measures, median and maximum degree, give insight into the degree distribution of the332 synthetic graphs, because together they partially capture the expected log-normal shape of the empirical333 network’s degree distribution [55]. Here, the DCSBM and SENCA outperform the SBM, ERM and NCRG334 (Fig 2). This is to be expected, as these two generators explicitly model the degree distribution of the335 empirical network. The NCRG particularly overestimates median degree (μ med = 47.09) and maximum336 degree (μ max = 170.14), again likely linked to its overestimation of edges. The SBM and ERM both slightly337 overestimate median degree (μ med = 14.34 andμ med = 14.80 respectively) while underestimating maximum338 degree (μ max = 34.36 and μ max = 26.10 respectively). The SENCA generates an average median and339 maximum degree of 11.63 and 57.4 respectively, closely resembling the empirical observations of 11.0 and 64340 respectively. However, this model shows considerable variation in its median degree and has a high number 341 of maximum degree outliers that overestimate the maximum degree in relation to the empirical maximum 342 degree by up to 11.6% compared to only 0.72% for the DCSBM. The DCSBM is overall much stabler in its343 performance and yields statistics (μ med = 10.97 andμ max = 54.5) that equally closely resemble the empirical344 network, but with more consistency and less variation across graphs in comparison to SENCA-generated345 graphs.346 In addition, the DCSBM follows the shape of the empirical degree distribution most closely (Fig 3 and347 October 12, 202616/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

Table 2). As expected, the ERM and SBM follow a Poisson rather than log-normal degree distribution 348 pattern, representing the homogeneity of this measure over the whole network (ERM) and within349 communities (SBM). The SENCA produces a higher number of individuals with zero connections, likely350 because edges are initially created based on the scaled Euclidean distance between two nodes. As a result,351 there might be a higher-than-expected number of individuals who are far removed from others and hence352 have no neighbors. In contrast, the NCRG underestimates the number of individuals with few connections,353 but yields a thicker and longer tail with degrees not observed in the empirical network. Kolmogorov-Smirnov354 distances between the synthetic and empirical degree distributions further confirm this pattern (S3 Fig).355 Overall, these data imply that while the DCSBM generator does not perform best in each separate network356 measure, it does appear to best capture both global (clustering) and local (degree and betweenness)357 heterogeneity in the empirical network.358 Fig 3. Summary of degree distributions across 5000 iterations of each graph type.Each point on the x-axis summarizes the distribution of frequency values observed across all graphs of a given graph type for a specific degree value. The shaded band indicates the interquartile range (25th to 75th percentile) and the solid line shows the median. The inset in the top right corner provides a zoomed-in perspective on the graph where the x-axis lies between 0 and 30. Comparing the performance of the graphs across all measures, we found that the DCSBM yielded the359 lowest Mahalanobis distance of 17.57, followed by the SBM with 20.98 and the SENCA with 29.21. The360 NCRG and ERM differ most, yielding distances of respectively 188.74 and 220.67. These gaps between361 generator means are large relative to within-generator variance, as visible in the per-measure distributions of362 Fig 2, so the ranking is unlikely to be a sampling artifact. While the ERM’s extreme statistic may be due to363 its lack of clustering and its strongly deviating degree distribution, the NCRG appears to over-correct for364 clustering and therefore inflates the empirical degree distribution. Taken together, the DCSBM graph365 generator performs best in reconstructing the empirical network’s overall structural network properties and366 capturing its heterogeneity.367 Epidemic dynamics across network topologies368 In the SEIR simulation (γ= 2), the time-averaged prevalence ( ̄ I) and peak prevalence (I max ) largely exhibit369 consistent trajectories across most graph types. In the empirical network outbreaks, low transmission rates370 (0< β≤0.03) generate near-zero average and peak prevalence. This is followed by a sharp nonlinear371 inflection betweenβ= 0.03 andβ= 0.07, marking the onset of major outbreaks. At higher transmission372 rates, growth decelerates as the shrinking pool of susceptible individuals leads to network saturation (Fig 4A).373 The SBM and DCSBM configurations most closely capture the empirical network’s outbreak dynamics.374 October 12, 202617/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

The SBM exhibits a minor delay in reaching the epidemic threshold untilβ= 0.07, but then rapidly375 converges with the DCSBM and empirical network (Fig 4A). The DCSBM captures the empirical average376 and peak prevalence very well, despite slight inflation forβ >0.08 for average prevalence andβ >0.13–0.14377 for peak prevalence. The ERM displays a minor delay, but subsequently increases more sharply beyond 378 β = 0.07. This accelerated transmission is likely driven by the model’s generation of short path lengths,379 which facilitate rapid transmission throughout the network in the absence of local clustering constraints.380 Conversely, the SENCA consistently overestimates outbreak prevalence across all transmission rates. The381 higher number of active cases in this model is an expected consequence of its higher average degree and lack382 of local clustering, both of which remove barriers to transmission provided the initially infected node is not383 isolated. The NCRG deviates more from these patterns. At a near-zero transmission rate (β= 0.01), its high384 edge density and triangular structures circumvent the typical threshold bottleneck. It consistently maintains385 an approximately 10–13% higher average and peak prevalence in comparison to the other graph types, which386 can likely be attributed to its comparatively high number of transmission paths.387 Fig 4. Outbreak simulation outcomes for SEIR and SIS models. Outbreak dynamics are illustrated for the A) SEIR model withγ= 2, B) SIS model withγ= 3, and C) SIS model withγ= 9 using the average prevalence ( ̄ I), the peak prevalence (I max ) and the number of total infections (CI, as a fraction in A but count in B and C) for each of the five graph types in comparison to the empirical network across the full range of modeled transmission rates. Only outbreaks with at least one secondary infection are shown in this visualization. The empirical distribution of total number of unique infections (CI) is characterized by a transmission388 threshold at aroundβ= 0.03 with a median CI (Med CI ) of 0.021, followed by exponential growth up to389 β= 0.07 (Med CI = 0.545) after which it gradually slows to the point where higher transmission rates390 exhaust the majority of the available susceptible population (forβ= 0.20,Med CI = 0.885) (Fig 4A). While391 the other graph types generate a similar distribution shape, the NCRG again shows exponential growth even392 for low transmission rates, yielding median outbreak size of 72.8% forβ= 0.03. This surge stabilizes around393 β= 0.07 and does not increase much further forβ= 0.20 (Med CI = 0.936). The SENCA also initially rises394 faster, with a median 18.7% of the population having been infected forβ= 0.03, but slows down for higher395 transmission rates (Med CI = 0.757 forβ= 0.20). In contrast, the ERM has an initially delayed response396 (Med CI = 0.013 forβ= 0.03), followed by a drastic surge which continues to increase steadily and reaches397 nearly the entire population atβ= 0.20 (Med CI = 0.987). The SBM follows a fairly similar trajectory with398 an initial underestimation (Med CI = 0.013 forβ= 0.03), but inflates the empirical outbreak pattern for399 transmission rates higher than 0.05, ultimately reaching 94.9% of the population forβ= 0.20. The DCSBM400 best fits the empirical distribution for both lower (atβ= 0.03,Med CI = 0.021) and higher transmission401 October 12, 202618/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

rates (at β= 0.20,Med CI = 0.876), despite its slight overestimation in outbreak size of around 2% for402 0.06< β≤0.13.403 Comparing the SIS simulation with its lowest and highestγvalues to the SEIR simulation outbreaks, it is404 clear that the SIS model yields smaller differences in outbreak size across transmission rates regardless of the405 length of the infectious window (Fig 4B–C and S9 Fig for remainingγvalues). Forγ= 3, the ERM, SBM,406 and DCSBM all closely follow the empirical outbreak trajectory in all three output measures, with the407 DCSBM nearly perfectly following the empirical network. The NCRG shows a general overestimation of408 outbreak size, which is initially more pronounced but gradually decreases to around 1% or less forβ= 0.20.409 The SENCA also initially slightly overestimates prevalence and cumulative incidence forβ <0.05, but410 underestimates them for allβ >0.05 likely due to presence of isolated individuals. While the SBM and ERM411 follow the empirical outbreak trajectory, they inflate cases and infections by 1–2%, which again may be412 attributable to the higher average and median degree of individuals in these networks.413 Atγ= 9, the longer infectious period leads to a higher number of individuals being infected at any given414 time while simultaneously resulting in a lower total number of infections as the turnover of individuals is415 slower (Fig 4C). For this longer infectious period, the convergence between graph types is even higher. The416 SBM, ERM, NCRG, and DCSBM follow the empirical case pattern very well (forβ= 0.20,Med ̄ I is 0.708,417 0.711, 0.691 and 0.688 respectively compared to 0.697 in the empirical network). The SENCA is an exception418 to this trend; it again consistently and increasingly underestimates cases for higher transmission rates (for419 β= 0.20,Med ̄ I = 0.589). Hence, while the DCSBM remains among the closest to the empirical network420 across the full transmission rate range, this convergence likely reflects how heterogeneous network structure421 is no longer as crucial for transmission in a model without a removal state and with longer infectious periods.422 This may therefore lead to a homogenization of the case pattern and remove the influence of network hubs423 and super-spreader individuals.424 Outbreak classification and scale across network topologies425 The observed outbreak size patterns are inextricably linked to the outbreak duration too, particularly in the426 SEIR model where all outbreaks ended prior to reaching the maximum outbreak duration (Fig 5). We427 distinguished between minor and major outbreaks for each graph type andβcombination by identifying428 local peaks and their corresponding valleys (Materials and methods and S10 Fig). Atβ= 0.01, most graph429 types closely mirror the empirical network, with major outbreaks averaging 1.6–2.3% of the population over430 69–87 days and minor outbreaks remaining near-negligible (μ size ≈0.5%,μ duration ≈4.5 days). The NCRG431 is a clear exception: its major outbreaks already average 28.1±15.2% of the population and last 337.2±154.9432 October 12, 202619/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

days on average, reflecting the same threshold-bypassing pattern observed in the prevalence analysis driven433 by its high edge density and abundance of triangular structures (S5 Table). 434 Fig 5. SEIR final outbreak size and outbreak duration. Results are shown for three values ofβ representing its full modeled range, separated into minor and major outbreaks for outbreaks simulated with each graph type and the empirical network. The x-axis shows outbreak duration measured in days (maximum = 1000) and the y-axis shows the final outbreak size measured as the proportion of removed individuals at the final day of the outbreak. Major outbreaks are indicated with darker shading compared to minor outbreaks. At β = 0.1, the empirical network separates into two distinct clusters, with major outbreaks containing 435 on average 71.5±5.3% of the population and lasting on average 319.9±68.6 days (S10 Fig and S5 Table). The436 DCSBM and SBM reproduce this pattern most closely (average major outbreak size: 73.1±4.4% and437 80.5±5.1%; average duration: 311.9±61.2 and 362.9±77.0 days respectively), with the SBM exhibiting438 slightly more size variability and a higher maximum final outbreak size (92.3% versus 85.5%). The SENCA439 produces two clusters that are more concentrated, yielding a slightly lower average size of 67.8±2.5% and440 substantially shorter average duration of 213.0±31.3 days consistent with earlier susceptible population441 exhaustion. The NCRG exhibits more divergence between minor and major outbreaks. On average, its442 outbreaks are larger (90.3±1.4%) but of substantially shorter and less variable length (149.6±18.5 days).443 Lastly, the ERM shows a similar gap between minor and major outbreaks (89.9±2.8%) and a more444 comparable duration (313.4±51.3 days) to the empirical scenario (S5 Table).445 Atβ= 0.2, clusters concentrate further: empirical outbreaks average 88.7±2.6% of the population over446 254.9±45.0 days, while minor outbreaks average 0.5±0.5% of the population over 3.8±12.0 days (S5 Table).447 The DCSBM again fits most closely (major outbreaks:μ size = 88.3±2.1%,μ duration = 227.9±34.7 days;448 minor outbreaks:μ size = 0.5±0.2%,μ duration = 2.9±8.5 days), but yields a more concentrated distribution449 of values (S10 Fig and S5 Table). The SBM also captures the empirical patterns well, though with slightly450 higher major outbreak sizes (μ size = 95.2±1.9%,μ duration = 254.9±41.1 days) and shorter minor outbreaks451 (μ size = 0.5± 0.2%, μ duration = 2.9± 9.2 days). The SENCA overall produces shorter, smaller and less452 variable outbreaks of both types (major outbreaks:μ size = 76.2±2.0%,μ duration = 163.2±20.5 days; minor453 outbreaks: μ size = 0.4± 0.1%, μ duration = 2.2± 5.2 days). The ERM generates major outbreaks that454 encompass nearly the entire population and are most homogeneous across iterations (μ size = 98.9±0.7%,455 μ duration = 193.8±23.5 days) and generates relatively small and short minor outbreaks (μ size = 0.4±0.1%,456 μ duration = 1.9± 6.0 days). Lastly, the NCRG portrays a similar pattern as for β= 0.1, but with larger457 major outbreaks (μ size = 94.2±0.9%,μ duration = 123.6±17.6 days) and comparably similar minor458 outbreaks (μ size = 0.4±0.1%,μ duration = 2.0±5.9 days).459 October 12, 202620/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

Across all these transmission rates, the DCSBM most consistently reproduces the empirical distribution460 of outbreak sizes and durations. The SBM performs comparably to the DCSBM but inflates major outbreak461 size, particularly atβ= 0.2. The ERM and NCRG both overestimate major outbreak saturation,462 particularly at a higher transmission rate, while the SENCA systematically underestimates outbreak463 duration, likely reflecting the structural constraints discussed above.464 Generalizability across empirical and simulated scenarios465 To test whether the patterns found so far are network-specific, we compared four additional proximity-based466 dog interaction networks of varying sizes, number of connected components, and degrees of clustering (S11467 Fig). The Romana and Hepang networks contain fewer nodes compared to the empirical (Chad), Sabaneta468 and Habi networks, while these three networks are characterized by lower edge density (Table 4). Moreover,469 the Habi and Romana networks are both fully connected, whereas the Hepang and Sabaneta networks each470 contain one major component encompassing nearly all nodes and a smaller isolated cluster, similar to the471 thus far examined Chad network.472 Examining the network topology for each of the four networks, the DCSBM overall best captures empirical473 maximum and median degree and most closely reproduces each network’s overall degree distribution, yielding474 the lowest K-S distances to empirical degree distributions among all graph types (Table 4 and S12 Fig–S14475 Fig). The ERM and SBM produce similar mean and median degree outcomes. The SENCA varies in its476 degree outcomes, underestimating degree in the smaller Hepang and Romana networks, while overestimating477 it in the larger but lower-density Sabaneta and Habi where it also underestimates betweenness and clustering.478 This effect is most severe for Habi, the lowest density network. The NCRG consistently overestimates degree479 statistics, particularly median and maximum degree in Sabaneta and edge density in Hepang and Romana.480 With the exception of average betweenness, it performs best in reproducing Habi’s topology in comparison to481 the other networks. These patterns reflect the same tendency seen in the Chad network to generate482 triangular structures and high-degree hubs regardless of the empirical degree distribution.483 In comparison to degree measures, mean betweenness and global clustering vary more across graph types.484 The synthetic Romana networks yield narrow mean betweenness distributions closely resembling the485 empirical network, but for Habi and Sabaneta they mostly underestimate mean betweenness. The SBM yields486 the highest mean betweenness overall, while the NCRG, SENCA and ERM produce lower values, particularly487 in less dense networks. The SBM, SENCA and ERM strongly underestimate global clustering. The DCSBM488 also systematically underestimates global clustering, but yields estimates far closer to the empirical values,489 competing with the NCRG for better performance between network locations. The NCRG does not produce490 October 12, 202621/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

Table 4. Empirical network metrics, synthetic-model medians and Mahalanobis distance (D 2 ) across the five empirical locations.For each location, the table reports median values across 5000 graph iterations for six network measures (density, global clustering, mean betweenness, mean degree, median degree, maximum degree) for each generator alongside the empirical value, and the Mahalanobis distance summarizing the multivariate gap between each generator’s measure distribution and the empirical reference. LocationParameterEmpiricalERMSBMDCSBMNCRGSENCA ChadDensity0.0630.0630.0630.0600.2380.067 (Nodes: 235) Global Clustering0.4040.0630.2040.2850.5450.178 (Edges: 1739) Mean Betweenness215.089152.681 190.555 183.02691.162 102.653 Mean Degree14.80014.800 14.80413.94955.61715.664 Median Degree11.00015.000 14.00011.00047.00012.000 Max. Degree64.00026.000 34.00054.000 170.00057.000 Mahalanobis D 2 —220.673 20.98417.570 188.74129.208 RomanaDensity0.1720.1720.1720.1640.3930.085 (Nodes: 57)Global Clustering0.3920.1720.1970.2990.5970.193 (Edges: 275) Mean Betweenness29.82527.526 28.24629.91215.45631.333 Mean Degree9.6499.6499.6499.19322.0004.772 Median Degree8.00010.000 10.0008.00022.0004.000 Max. Degree27.00016.000 16.00024.00044.00015.000 Mahalanobis D 2 —18.963 15.7905.27767.8964.731 SabanetaDensity0.0650.0650.0650.0630.1650.098 (Nodes: 121) Global Clustering0.3780.0640.1850.2310.3750.177 (Edges: 471) Mean Betweenness121.18292.802 117.273 116.22365.93476.963 Mean Degree7.7857.7857.7857.56219.83511.719 Median Degree7.0008.0008.0007.00018.00011.000 Max. Degree27.00015.000 17.00026.00072.00028.000 Mahalanobis D 2 —53.696 14.7719.79174.23820.624 HabiDensity0.0540.0540.0540.0500.0980.158 (Nodes: 81)Global Clustering0.4190.0530.1910.2710.3460.235 (Edges: 176) Mean Betweenness120.59382.185 98.23584.58059.82141.000 Mean Degree4.3464.3464.3214.0257.82712.667 Median Degree4.0004.0004.0003.0005.00012.000 Max. Degree14.00010.000 10.00014.00027.00027.000 Mahalanobis D 2 —27.9677.5145.74130.21019.311 HepangDensity0.1190.1190.1190.1050.2400.081 (Nodes: 61)Global Clustering0.4630.1170.2970.3800.5330.193 (Edges: 217) Mean Betweenness43.37738.311 53.95149.24623.70534.967 Mean Degree7.1157.1157.1156.29514.3934.885 Median Degree6.0007.0007.0005.00011.0004.000 Max. Degree34.00013.000 15.00025.00041.00016.000 Mahalanobis D 2 —27.536 14.8655.51936.0209.917 such a consistent pattern, overestimating clustering for some and underestimating it — albeit only slightly —491 for others. Its higher performance for this metric is no surprise, as the model is designed to capture this492 metric. Still, the DCSBM is able to yield nearly comparable clustering without optimizing for it. In493 combination with its consistent improvement over the SBM and the inability of the other synthetic graphs to494 reproduce clustering, this suggests that a) clustering does not need to be specifically targeted for realistic495 October 12, 202622/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

clustering estimates to emerge and b) degree heterogeneity plays an important role in modeling empirical496 transitivity patterns. This conclusion is further supported by the DCSBM’s lower Mahalanobis distance to497 the empirical network’s combined summary measures at every location except Romana (Table 4).498 These structural differences impact outbreak dynamics. The two lower density networks (Habi and499 Sabaneta) produce simulated empirical rabies outbreaks with lower average and peak prevalence than500 Hepang and Romana (Fig 6). The ERM, SBM, and DCSBM largely follow the simulated outcomes of the501 empirical network, particularly for average and peak prevalence measures. The NCRG and SENCA diverge502 more, where the NCRG consistently overestimates all outbreak metrics when compared to the empirical 503 network, only coming close to empirical estimates of total infections (CI) in the Romana network for larger504 transmission rates. The SENCA yields more variable outcomes, matching the NCRG’s overestimation for the505 Habi and Sabaneta networks while underestimating prevalence for the Romana network. Interestingly, it506 closely matches Hepang’s empirical outbreak dynamics. These variable outcomes are likely attributable to507 how the SENCA models edge density in these networks: it overestimates edge density in the former two508 networks, yielding more transmission pathways, while underestimating it for the Romana and Hepang509 networks.510 Overall, the ERM does an acceptable job at reproducing outbreak dynamics, though it inflatesCIfor511 high transmission rates in all four networks. It yields considerably higherCIin the Habi, Sabaneta and512 Hepang networks forβ >0.15, most likely driven by its short path lengths in the absence of modeled513 clustering. The SBM and DCSBM perform consistently well and produce comparable outbreak dynamics514 outcomes, portraying only negligible differences in favor of the DCSBM. Together, these findings highlight515 how the DCSBM consistently reproduces both empirical network topology and outbreak dynamics, thereby516 supporting its applicability beyond a single network.517 Fig 6. SEIR outbreak dynamics for each location per graph type.Panels visualize the relationship between transmission rate and average and peak prevalence as well as the total infections (CI) for each location network, separated into minor (dashed line) and major (solid line) outbreaks. Discussion518 In this study, we evaluated five network generator algorithms for network reconstruction in rabies519 transmission modeling, demonstrating how structural choices in network reconstruction can alter outbreak520 predictions as substantially as the biological parameters of the disease model itself. Across both static521 topological metrics and stochastic outbreak simulations, the degree-corrected stochastic block model was the522 October 12, 202623/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

most consistent at reconstructing free-roaming dog contact networks and reproducing their empirical rabies523 transmission dynamics. Crucially, this consistency was robust across five distinct empirical networks of 524 varying size, density, and connectedness.525 Contrasting the performance of the DCSBM against the other four network generators reveals the relative526 contributions of three fundamental axes of network heterogeneity: degree heterogeneity, community structure,527 and local clustering. Comparing the DCSBM to the standard SBM demonstrates how modeling within-block528 degree heterogeneity on top of community structure improves both topological and epidemiological fit.529 Conversely, the contrast between the DCSBM and SENCA illustrates the substantial explanatory value of530 community structure beyond degree heterogeneity alone. The comparison with the NCRG introduces a third531 axis: explicit triadic closure, which the DCSBM does not model natively. Although local clustering is a532 well-documented empirical feature of interaction networks, network reconstruction based on triadic533 membership alone did not outperform the implicit clustering that naturally emerges from combining degree534 heterogeneity with community structure within the DCSBM framework. The NCRG produced the most 535 pronounced deviations from empirical outbreak dynamics, a direct consequence of its high edge density and536 abundance of triangular structures generating transmission pathways that circumvent the barriers present in537 the empirical network.538 The NCRG outcome suggests a more general working hypothesis worth testing in future work: that the539 three axes of degree heterogeneity, community structure, and clustering do not decompose orthogonally as540 independent reconstruction targets. The NCRG isolates clustering and produces a roughly fourfold edge541 inflation relative to the empirical network (mean degree 55.6 vs empirical 14.8; density 0.24 vs empirical542 0.06), and the implicit clustering that emerges from the DCSBM’s joint coupling of degree heterogeneity with543 community structure (mean global clustering 0.29) is closer to the empirical value (0.40) than the NCRG’s544 explicit target-clustering value (0.54). This pattern is consistent across all five empirical locations examined545 here (Table 4), where the DCSBM achieves Mahalanobis distances several-fold smaller than the NCRG’s at546 every location, though the NCRG yields slightly more accurate clustering estimates for 3 out of 5 locations.547 We frame this as a working hypothesis rather than an established principle because our evidence rests on a548 single network family (free-roaming dog proximity contacts in five geographic settings), and the joint-stub549 formulation we implemented is one of several possible NCRG-class constructions. If the hypothesis is borne550 out by independent testing in other empirical network families, it would imply that orthogonal-axes 551 generator-comparison frameworks materially understate the difficulty of network reconstruction, and that552 practical generator selection should weight joint structural coupling more heavily than independent feature553 targeting.554 October 12, 202624/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

Importantly, the influence of these structural choices is not static; rather, it is highly dependent on the555 life-history parameters of the disease model. While degree heterogeneity and community structure are556 recognized as foundational drivers of outbreak dynamics and intervention design [11, 16, 21], our SIS557 sensitivity analyses with varying infectious periods reveal that this topological influence progressively558 weakens as the infectious window lengthens. At a nine-day infectious period, average and peak prevalence559 trajectories converged across nearly all generators ( ̄ I≈0.69 to 0.71 atβ= 0.20, all within roughly two560 percentage points of the empirical value of 0.697), even as their underlying topological signatures remained561 clearly distinct. The SENCA remained the sole exception to this convergence, likely reflecting the influence562 of its smaller fully connected component.563 This convergence highlights how the extent to which contact network topology shapes outbreak dynamics564 depends on how the pathogen exploits that network. When infectious windows are short relative to typical 565 contact rates — as in canine rabies, where the symptomatic period averages only a few days due to human 566 recognition of behavioral symptoms and subsequent euthanasia — each infected individual can only make a567 limited number of transmission attempts. Under this assumption, the exact topological identity of those568 immediate contacts matters intensely. As the infectious window lengthens, however, infected individuals569 progressively exhaust their local network neighborhoods, and the precise ordering of contacts becomes less570 determinative of overall outbreak trajectory. Network reconstruction therefore appears most consequential571 for short-infectious-window pathogens like canine rabies, and progressively less so for slower-burning572 infections in which the pathogen has sufficient time to traverse the giant connected component regardless of573 local structure and bottlenecks. This pattern aligns with prior theoretical work on the relationship between574 infectious-window length and topological sensitivity [2, 19], and our results suggest the effect is large enough575 to inform generator selection in practical modeling applications. These implications extend past canine rabies576 to other short-infectious-window infectious diseases where network-based control strategies are actively577 considered.578 Several limitations bound these findings. The first considers spatial scale. All five empirical networks579 contain between 57 and 235 nodes; whether the generator rankings established at this scale hold for city-scale580 populations of thousands of dogs — the regime relevant to large-scale mass vaccination programs — remains581 untested. Stochastic block model inference becomes computationally demanding at that scale, and582 triangle-based generators face parallel scaling constraints. A second limitation involves network sampling.583 While the spatiotemporal tracking of contact networks has advanced via GPS and other real-time location584 systems through increased positional accuracy and shorter temporal intervals [56–59], empirical data remains585 restricted to a participating or captured subset of the (animal) population. This introduces an inevitable586 October 12, 202625/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

trade-off between sampling coverage, duration, and frequency [1, 3, 28, 60–62], leading to restrictions in587 estimates of epidemic outbreaks by potentially masking the true outbreak size and duration through missing588 nodes and edges [60, 61]. Crucially, our evaluation framework treats the sampled empirical network as an 589 absolute baseline. Consequently, while a generator like the DCSBM may closely fit the observed empirical590 structures, those underlying structures may themselves be incomplete or biased representations of the total591 population of interest.592 Furthermore, because our five baseline networks were collected using identical geo-located proximity593 sensors over windows of several days using similar data collection protocols, it remains untested whether594 these generator rankings generalize to broader telemetry, observational, or self-reported data styles. Short595 observation windows may yield reasonably reliable degree-distributions, but accurately estimating community596 boundaries requires capturing enough repeated within-block contacts, just as calculating local clustering 597 depends on capturing explicit triadic closures. The relative rankings among generators may therefore reflect598 a confluence of how well each generator’s signature features can be inferred from the available data alongside599 how those features are actually expressed in the true population. A further constraint is that the SEIR 600 analysis relied on a single infectious period (γ= 2 days, the empirically established symptomatic-to-removal601 window for rabies in this setting), meaning that continuous γ-sensitivity probed by the SIS sweep is not602 directly mirrored in the SEIR comparison. Moreover, the Poisson-modeled latent period in the SEIR model603 (mean 30 days, standard deviation≈5.5) captures most but not all of the reported variation, omitting the604 long tail of incubation periods extending up to 125 days [52]; however, this tail is unlikely to alter the605 comparative structural performance of the generators evaluated in this study. Lastly, the empirical canine606 rabies outbreaks are still simulation-based only and are not cross-referenced or correspond to real-life607 outbreaks, and may thus not necessarily be fully representative of observed canine rabies outbreak dynamics.608 Beyond the substantive findings on generator choice, the data-driven kernel-density-valley approach used609 here to classify outbreaks as minor or major (see Materials and methods) is itself a small methodological 610 contribution. The standard alternatives in the network-epidemic literature are arbitrary thresholds (for611 example, declaring any outbreak that infects more than 10% of the population a ‘major’ outbreak). The612 kernel-density approach instead locates the threshold at the natural valley between the bimodal density613 modes that arise in stochastic outbreak ensembles, which removes a researcher degree of freedom and is614 robust to the bandwidth choice across the range we tested. The approach should transfer to any615 network-epidemic study where the bimodal minor/major structure is present, and provides a more principled616 basis for outbreak classification in cross-generator comparisons of the kind performed here.617 Several extensions follow naturally from this work. The most pressing is scaling these models up to618 October 12, 202626/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

city-level populations, the scale at which rabies vaccination programs typically operate but where generating619 networks with realistic edge and community densities becomes computationally demanding. A second 620 concerns ecological fidelity: our unweighted proximity-network framework cannot capture the full social or621 spatial complexity of free-roaming dog systems, nor does it currently extend to companion-dog populations622 whose contacts are mediated by households, dog parks, and veterinary facilities. Extending this comparative623 framework to weighted, temporal, multilayer or scalable networks would represent a major step forward.624 Finally, applying the framework to other proximity-transmitted infectious diseases, such as toxoplasmosis,625 brucellosis or Ebola, would clarify how broadly the generator rankings transfer to other disease systems.626 Taken together, our results contribute three insights to the network epidemiology of contact-transmitted627 infectious diseases. First, they identify the degree-corrected stochastic block model as the most structurally628 and epidemiologically consistent of the five generators tested for reconstructing free-roaming dog contact629 networks, with its performance advantage arising from the joint representation of degree heterogeneity and630 community structure. Second, they provide an empirically grounded criterion — pathogen-dependent631 topological sensitivity — for determining when generator selection is consequential and when simpler632 generators suffice: for short-infectious-window pathogens such as canine rabies, generator choice can633 substantially shift cumulative incidence and outbreak-duration predictions, whereas for longer infectious634 windows, predictions gradually converge across generators to within roughly two percentage points of the635 empirical reference for a window of nine days. This indicates that generator choice matters most precisely for636 acute, rabies-like pathogens, while differences largely attenuate for longer-burning infections. Third, the637 results motivate a working hypothesis concerning the non-orthogonality of structural axes in network638 reconstruction: the implicit clustering that emerges from jointly modeling degree and community structure639 reproduces empirical network structure more faithfully than explicit clustering targeted in isolation,640 suggesting that frameworks that treat structural dimensions as independent may materially understate the641 difficulty of network reconstruction. Together, these findings support the use of degree-corrected stochastic642 block models for network-based modeling and intervention design in canine rabies and comparable infectious643 disease systems.644 Supporting information645 S1 Fig. Network topology summaries per graph type for different seed run sizes.646 S2 Fig. Cumulative average of mean betweenness and degree.Running means for all graph types647 for four seed sizes ranging between 100 and 5000.648 October 12, 202627/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

S3 Fig. Kolmogorov–Smirnov distances to the empirical degree distribution.Distributions of the649 Kolmogorov-Smirnov distances between each synthetic degree distribution and the empirical degree650 distribution computed for all distributions of the different seed totals.651 S4 Fig. Schematic representations of the SIS (top) and SEIR (bottom) compartmental652 disease transmission models.State variables and parameter values are defined in S2 Table and S3 Table.653 S5 Fig. Factorial outbreak sampling results.Outbreak simulation outcomes under the factorial654 sampling design for the SIS and SEIR models at theγvalues indicated in each panel. Panels show (from left655 to right) average prevalence, peak prevalence, and cumulative incidence for each of the five graph types in656 comparison to the empirical network. Only outbreaks with at least one secondary infection are shown.657 S6 Fig. Factorial sampling SEIR outbreak results.SEIR final outbreak size and outbreak duration658 for three values ofβ, representing its full modeled range, separated into minor and major outbreaks for659 outbreaks simulated with each graph type and the empirical network. The x-axis shows outbreak duration660 measured in days (maximum = 1000) and the y-axis shows the final outbreak size measured as the661 proportion of removed individuals at the final day of the outbreak. Major outbreaks are indicated with662 darker shading compared to minor outbreaks.663 S7 Fig. Factorial sampling SIS outbreak results.SIS model summary of prevalence and total664 infections for remaining gamma values highlighting the increase in prevalence and decrease in total number of665 cases as γincreases.666 S8 Fig. Summary of betweenness distributions across 5000 iterations of each graph type.Each667 point on the x-axis summarizes the distribution of frequency values observed across all graphs of a given668 graph type for a specific betweenness value. The shaded band indicates the interquartile range (25th to 75th669 percentile) and the solid line shows the median.670 S9 Fig. SIS model summary of prevalence and total infections for remaining gamma values.671 These results highlight the increase in prevalence and decrease in total number of cases asγincreases.672 S10 Fig. Final outbreak size and outbreak duration of minor and major outbreaks for673 different transmission rates and for each graph type.674 October 12, 202628/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

S11 Fig. Single graph representations of additional empirical contact networks and 675 corresponding synthetic networks from each graph type.Networks shown for: A) Habi, B) Hepang,676 C) Sabaneta, D) Romana.677 S12 Fig. Distributions of six network parameters for all additional locations.The six measures678 include network density, global clustering, average betweenness, average degree, median degree, and679 maximum degree. Results are shown for all 5000 graph iterations of each graph type as well as their observed680 values in the empirical network for all four additional network locations.681 S13 Fig. Degree distribution over 5000 iterations of each graph type for all four additional682 network locations on a log-scale.683 S14 Fig. Kolmogorov-Smirnov distances for the degree distributions of all additional684 locations.The graph shows the distributions of the Kolmogorov-Smirnov distances between each synthetic685 degree distribution and the empirical degree distribution computed for all four additional network locations.686 S1 Table. Convergence analysis across graph types.Standard error, stepwise mean drift and687 precision gain for mean degree and mean betweenness across sample sizes.688 S2 Table. State variables for the SIS and SEIR models.689 S3 Table. Parameter values for the SIS and SEIR models.690 S4 Table. Definitions and epidemiological significance of calculated network metrics.691 S5 Table. Size and duration of minor and major SEIR outbreaks.Mean and standard deviation of692 final outbreak size and duration per graph type and transmission rate.693 Acknowledgments694 The simulations presented in this manuscript were performed on the sciCORE scientific computing cluster of695 the University of Basel (http://scicore.unibas.ch/). We thank the data collection teams whose696 proximity-sensor fieldwork in Chad, Indonesia, and Guatemala made this study possible. We thank Dr.697 Mirjam Laager for the consultations on her published work and Professor Jakob Zinsstag for data access and698 consultation.699 October 12, 202629/37 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

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.CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

.CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint

.CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 22, 2026. ; https://doi.org/10.64898/2026.10.16.759544doi: bioRxiv preprint