Online Appendices, Not for Publication

In this section, we provide basic definitions and interpretations for the different network characteristics that we consider. At the household level, we study: • Degree: the number of links that a household has. This is a measure of how well connected a node is in the graph. • Clustering coefficient: the fraction of a household’s neighbors that are themselves neighbors. This is a measure of how interwoven a household’s neighborhood is. • Eigenvector centrality: recursively defined notion of importance. A household’s importance is defined to be proportional to the sum of its neighbors’ importances. It corresponds to the ith entry of the eigenvector corresponding to the maximal eigenvalue of the adjacency matrix. This is a measure of how important a node is, in the sense of information flow. We take the eigenvector normalized with ‖·‖2 = 1. • Reachability and distance: we say two households i and j are reachable if there exists a path through the network which connects them. The distance is the length of the shortest such path. At the hamlet level, we consider: • Average degree: the mean number of links that a household has in the hamlet. A network with higher average degree has more edges on which to transmit information. • Average clustering: the mean clustering coefficient of households in the hamlet. This measures how interwoven the network is. • Average path length: the mean length of the shortest path between any two households in the hamlet. Shorter average path length means information has to travel less (on average) to get from household i to household j. • First eigenvalue: the maximum eigenvalue of the adjacency matrix. This is a measure of how diffusive the network is. A higher first eigenvalue tends to mean that information is generally more transmitted. • Fraction of nodes in the giant component: the share of nodes in the graph that are in the largest connected component. Typically, realistic graphs have a giant component with almost all nodes in it. Thus, the measure should be approaching one. For a network that is sampled, this number can be significantly lower. In particular, networks which were tenuously or sparsely connected, to begin with, may “shatter” under sampling and therefore the giant component may no longer be giant after sampling. In turn, it becomes a useful measure of how interwoven the underlying network is. • Link density: the average share of connections (out of potential connections) that a household has. This measure looks at the rate of edge formation in a graph.