Portraits of Complex Networks

TL;DR

This paper introduces a novel matrix-based method for characterizing, visualizing, and comparing large complex networks, enabling insights into their structure and dynamics, with applications in graph theory and network analysis.

Contribution

A new matrix structure that uniquely encodes network information, facilitating visualization, comparison, and analysis of large complex networks.

Findings

Effective visualization of large networks using the new matrix

Ability to compare networks statistically using the matrix

Applications demonstrated in graph theory and network similarity testing

Abstract

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animations. Applications to graph theory are discussed, as are generalizations to weighted networks, real-world network similarity testing, and applicability to the graph isomorphism problem.