On the information-theoretic formulation of network participation

TL;DR

This paper introduces an information-theoretic approach to measure node connection diversity in networks, generalizing existing metrics and enabling analysis of complex connection patterns using entropy-based metrics.

Contribution

It develops a formalism linking participation coefficient to participation entropy and introduces new joint and conditional entropy metrics for network analysis.

Findings

Participation coefficient is a first-order approximation of participation entropy.

New entropy-based metrics capture complex connection patterns.

Formalism enables analysis of subtle nodal connection structures.

Abstract

The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here as participation entropy, has been introduced as the Shannon entropy of the distribution of module labels across a node's connected neighbors. While diversity metrics have been studied theoretically in other literatures, including to index species diversity in ecology, many of these results have not previously been applied to networks. Here we show that the participation coefficient is a first-order approximation to participation entropy and use the desirable additive properties of entropy to develop new metrics of connection diversity with respect to multiple labelings of nodes in a network, as joint and conditional participation entropies. The information-theoretic formalism developed here allows new and more subtle types of nodal connection patterns in complex networks to be studied.