Laplacian paths in complex networks: information core emerges from entropic transitions

TL;DR

This paper introduces a novel theoretical framework for analyzing information diffusion in complex networks, revealing how information pathways and cores emerge across multiple scales, with implications for understanding network synchronization and structure.

Contribution

The study develops new methods to quantify information diffusion, identify critical network scales, and uncover the information core, advancing the analysis of complex network structures and dynamics.

Findings

Identification of the information core as a mesoscale structure

Demonstration of scale-dependent information flow patterns

Relevance of information pathways to synchronization phenomena

Abstract

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues. We employ a variety of brand-new theoretical techniques allowing for: (i) bring the theoretical framework to quantify the probability of information diffusion among nodes, (ii) identify critical scales and structures of complex networks regardless of their intrinsic properties, and (iii) demonstrate their dynamical relevance in synchronization phenomena. By combining these ideas, we evidence how the information flow on complex networks unravels different resolution scales. Using computational techniques, we focus on entropic transitions, uncovering a generic mesoscale object, the information core, and controlling information processing in complex networks. Altogether, this study sheds much light on allowing new theoretical techniques paving the way to introduce future renormalization group approaches based on diffusion distances.