A Probabilistic Algorithm to Estimate the Spectral Moments of Large Undirected Weighted Graphs

Complex networks are often used to model real systems. Examples of such networks include computer networks, cities in a state or countries interconnected by highways, the connection between neurons in the brain, atoms in a molecule, and relations between people in a social network. A graph can represent any complex network, and we can use a matrix to represent a graph. Graph spectrum is the eigenvalues of the matrix associated with the graph, and the spectral moments are the moments of the distribution of these eigenvalues. The spectral moments give us intuitions about the shape of the distribution of the eigenvalues, and it can be used to study complex networks. In this work, we show an algorithm (implemented in C) that can efficiently estimate the spectrum moments of an undirected weighted graph. The implementation of this algorithm is freely available to download at GitHub (https://github.com/GuDiasOliveira/graph-spectral-moments).