Centrality measures.

In matrix notation: x is the vector of node centralities, A is the graph adjacency matrix, λ1 is the largest eigenvalue of A, D is the degree matrix (the diagonal matrix of node degrees), 1 is the vector of ones, and I is the identity matrix (the diagonal matrix of ones). Other notation: dij is the number of edges on the shortest path between nodes i and j, σjk is the number of shortest paths between nodes j and k, σjk|i is the number of shortest path between nodes j and k which pass through i.