An information-theoretic, all-scales approach to comparing networks

TL;DR

This paper introduces the Network Portrait Divergence, a new, mathematically principled measure for comparing networks across all structural scales, applicable to various network types and useful for analyzing complex, multilayer, and temporal networks.

Contribution

It presents a novel, all-scales network comparison measure based on the network portrait, addressing a key open problem in network analysis.

Findings

Effective in distinguishing synthetic and real-world networks

Reveals characteristics of multilayer and temporal networks

Applicable across diverse network types

Abstract

As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is network comparison, developing a similarity or distance measure between networks so that meaningful comparisons can be drawn. The best means to accomplish this task remains an open area of research. Here we introduce a new measure to compare networks, the Network Portrait Divergence, that is mathematically principled, incorporates the topological characteristics of networks at all structural scales, and is general-purpose and applicable to all types of networks. An important feature of our measure that enables many of its useful properties is that it is based on a graph invariant, the network portrait. We test our measure on both synthetic graphs and real world networks taken from protein interaction data, neuroscience, and computational social science applications. The Network Portrait Divergence reveals important characteristics of multilayer and temporal networks extracted from data.