An information-geometric approach for network decomposition using the q-state Potts model

TL;DR

This paper introduces an information-geometric method for decomposing labeled networks into low and high information subgraphs using a q-state Potts model, enhancing understanding of network modularity and structure.

Contribution

It presents a novel information-geometric framework for network decomposition based on the Potts model and Fisher information, enabling identification of informative nodes and network segmentation.

Findings

High information subgraph relates to edges and boundaries.

Low information subgraph provides a smoother, modular structure.

Method improves network understanding and modularity detection.

Abstract

Complex networks are critical in many scientific, technological, and societal contexts due to their ability to represent and analyze intricate systems with interdependent components. Often, after labeling the nodes of a network with a community detection algorithm, its modular organization emerges, allowing a better understanding of the underlying structure by uncovering hidden relationships. In this paper, we introduce a novel information-geometric framework for the filtering and decomposition of networks whose nodes have been labeled. Our approach considers the labeled network as the outcome of a Markov random field modeled by a q-state Potts model. According to information geometry, the first and second order Fisher information matrices are related to the metric and curvature tensor of the parametric space of a statistical model. By computing an approximation to the local shape operator, the proposed methodology is able to identify low and high information nodes, allowing the decomposition of the labeled network in two complementary subgraphs. Hence, we call this method as the LO-HI decomposition. Experimental results with several kinds of networks show that the high information subgraph is often related to edges and boundaries, while the low information subgraph is a smoother version of the network, in the sense that the modular structure is improved.