Patent Document ID: 9262380
Application ID: 13900040
Patent Flag: 1

Claim One:
1. A computer-implemented method, comprising: identifying one or more influences within a network, the identifying comprising: representing the network as a graph comprising a plurality of nodes, the graph being further represented by an adjacency matrix; multiplying a random probe vector v i by a resolvent function (A−zI) −1 , wherein A is the adjacency matrix, I is an identity matrix, and z is a selected scalar number using a result of the multiplying the random probe vector by the resolvent function as an approximation of a product of a matrix exponential and the random probe vector; computing, by a computer processor, a diagonal of the adjacency matrix based on the product of the matrix exponential and the random probe vector, wherein the computing comprises: initializing vectors Q, W, and D of length N to zero, wherein the vector D represents the diagonal; initializing the random probe vector v i ; computing the product of the matrix and the random probe vector; updating the vector Q by calculating Q=Q+v i .×Z, where Z is the product of the matrix and the random probe vector, wherein .x symbolizes element-wise multiplication; updating the vector W by calculating W=W+v i .×v i ; updating the vector D by calculating D=D+Q ./W, wherein ./ symbolizes element-wise division; and repeating the initializing the random probe vector, the computing the product, the updating the vector Q, the updating the vector W, and the updating the vector D until at least one of (a) the difference of a previously estimated diagonal and an estimated diagonal is smaller than a designated diagonal tolerance, and (b) a percentage of nodes with target centrality has converged; and calculating node centralities of the graph based on the computed diagonal of the adjacency matrix.