Free Energy and Network Structure: Breaking Scale-Free Behaviour Through Information Processing Constraints

TL;DR

This paper explains how the Free Energy Principle accounts for deviations from scale-free network behavior by modeling information processing constraints, revealing regimes that produce realistic degree distributions.

Contribution

It introduces a minimal FEP-based model that links agent information processing constraints to emergent network structures, explaining real-world deviations from scale-free patterns.

Findings

Identification of three distinct network regimes based on detection noise and processing limits.

Demonstration of super-linear growth leading to preferred cluster scales.

Explanation of knee-shaped degree distributions as signatures of optimal information processing.

Abstract

In this paper we show how The Free Energy Principle (FEP) can provide an explanation for why real-world networks deviate from scale-free behaviour, and how these characteristic deviations can emerge from constraints on information processing. We propose a minimal FEP model for node behaviour reveals three distinct regimes: when detection noise dominates, agents seek better information, reducing isolated agents compared to expectations from classical preferential attachment. In the optimal detection regime, super-linear growth emerges from compounded improvements in detection, belief, and action, which produce a preferred cluster scale. Finally, saturation effects occur as limits on the agent's information processing capabilities prevent indefinite cluster growth. These regimes produce the knee-shaped degree distributions observed in real networks, explaining them as signatures of agents with optimal information processing under constraints. We show that agents evolving under FEP principles provides a mechanism for preferential attachment, connecting agent psychology with the macroscopic network features that underpin the structure of real-world networks.