the betweenness centrality measure [38] , defined as the fraction of shortest paths a node falls on. While degree and betweenness centrality are often strongly positively correlated, the correlation between degree and betweenness centrality becomes weaker as community structure becomes stronger ( Figure 3 ). Thus, in networks with community structure, focusing on the degree alone carries the risk of missing some of the community bridges that are not highly connected. Indeed, at a low vaccination coverage, an immunization strategy based on betweenness centrality results in fewer infected cases than an immunization strategy based on degree as the magnitude of community structure increases ( Figure 4a ). This observation is critical because the potential vaccination coverage for an emerging infection will typically be very low. A third measure, random walk centrality, identifies target nodes by a random walk, counting how often a node is traversed by a random walk between two other nodes [39] . The random walk centrality measure considers not only the shortest paths between pairs of nodes, but all paths between pairs of nodes, while still giving shorter paths more weight. While infections are most likely to spread along the shortest paths between any two nodes, the cumulative contribution of other paths can still be important [40] : immunization strategies based on random walk centrality result in the lowest number of infected cases at low vaccination coverage (Figure 4b and 4c ).