| 主权项 |
1. A computer system, comprising:
a memory having computer readable computer instructions; and a processor for executing the computer readable instructions to perform a method comprising identifying one or more influencers 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 vi 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 a product of a matrix exponential and the random probe vector;computing 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 vi;computing the product of the matrix and the random probe vector;updating the vector Q by calculating Q=Q+vi .x 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+vi .x vi;updating the vector D by calculating D=D+Q ./ W, wherein ./ symbolizes element-wise division; andrepeating 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; andcalculating node centralities of the graph based on the computed diagonal of the adjacency matrix. |
