Figure 1: The top and bottom rows show the two kinds of mixing used, and the left and right panels show the block mixing structure and block mixing matrices, respectively. In all diagrams, the eight blocks represent the eight groups of nodes that partition each network. Panel a shows the random block structure, with lines connecting blocks that share edges. Panel b shows the corresponding mixing matrix, where the rows and columns represent each block, and color shade (see the color bar) represents the fraction of edges shared between members of each block. Panels c and d show the block mixing structure and matrices for the heterogeneous structure, respectively. Contagion Process Probability of Cluster Exposure The contagion process continues for T = 5 time steps. For simplicity, we assume a strong exposure effect that reduces contagious spread: the probability each affected node affects a selected neighbor is p$_{0}$ = 0 . 3 in unexposed clusters and p$_{1}$ = 0 . 1 in exposed clusters. The true simulation propensity score, the probability that a given cluster is exposed, is generated by a simple logistic function of a single cluster-level covariate, the number of affected neighbors at baseline summed for all nodes in each cluster (see Equation 3). For each scenario, ψ$_{0}$ and ψ$_{A}$ are selected such that this probability is between 0 . 1 and 0 . 9 for all clusters. In the estimation procedure, the regression used for the exposure propensity model includes this covariate, ensuring asymptotically unbiased estimation of the exposure effect. 11 HeterogeneousS tructur e RandomStructur e b a d c