Simplification of large networks and graphs

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 for reducing an original network, the method comprising:

utilizing the original network to model dynamics, wherein the original network has an original memory footprint in a computer system;

calculating node centralities of a graph until a designated number of central nodes are detected, wherein the graph represents the original network, and wherein the calculating of the node centralities of the graph further comprises:

approximating, by a processing device, a product of a matrix exponential and a random probe vector of an adjacency matrix, the adjacency matrix representing the graph; and

computing a diagonal of the adjacency matrix based on the product of the matrix exponential and the random probe vector;

selecting a percentage of the central nodes as pivot nodes;

collapsing neighboring nodes to each pivot node until the graph shrinks to a predefined threshold of total nodes;

determining a reduced graph resulting from the graph responsive to reaching the predefined threshold, wherein the reduced graph represents a reduced network having preserved connectivity information of the original network; and

reducing the original network to form a reduced network based on the reduced graph; and

utilizing the reduced network to model the dynamics, wherein the reduced network has a reduced memory footprint in the computer system as compared to the original footprint.

2. The computer system of claim 1 , wherein the collapsing further comprises:

acquiring a first set of neighboring nodes for each pivot node;

acquiring a second set of neighboring nodes for each node in the first set of neighboring nodes;

deleting the first set of neighboring nodes; and

establishing the second set of neighboring nodes as neighbors for a current pivot node.

3. The computer system of claim 2 , wherein the first set of neighboring nodes and the second set of neighboring nodes are not pivot nodes.

4. The computer system of claim 1 , wherein the approximating of the product of the matrix and the random probe vector further comprises:

computing an orthogonal Krylov basis and tridiagonal matrix using a Lanczos algorithm;

computing a matrix exponential of the tridiagonal matrix; and

computing a current approximation of the product of the matrix exponential and the random probe vector.

5. The computer system of claim 1 , wherein the computing of the diagonal further comprises calculating the diagonal based on a formula D s =SUM 1 s (v i .x F(A)v i ) ./ SUM 1 s (v i .x v i ), where D is a diagonal, v i is the random probe vector, s is the total number of required vectors, A is the adjacency matrix of size N, F(A) is the matrix exponential, .x symbolizes element-wise multiplication, and ./ symbolizes element-wise division.