The eigenvector centrality of a node, v, is proportional to the sum of the centrality scores of its neighbors. For example, the more important people you are connected to, the more important you are. This centrality measure is very interesting because an actor with a small number of hugely influential contacts might outrank ones with many more mediocre contacts. For our social network, it will hopefully allow us to get underneath the celebrity structure of heroic teams and see who actually is holding the social graph together.
To compute the eigenvector centrality, calculate the argmax of the eigendecomposition of the pairwise adjacency matrix of the graph. The ith element in the eigenvector gives the centrality ...
