for i?s, t. Here, A ij is the element in the adjacency matrix of the graph (0 or 1 in our case), and T is is the element in the voltage matrix which is calculated as described in detail in Newman [39] . Nodes are ranked according to the measure chosen (i.e degree, betweenness centrality, or random-walk centrality). We then immunize nodes going from high to low rankings, until the desired immunization coverage is achieved.