Optimization and Scale-freeness for Complex Networks

TL;DR

This paper explores how scale-free distributions in complex networks maximize information content, proposing a maximum entropy approach and validating predictions with metabolic network data.

Contribution

It introduces a maximum entropy framework for understanding scale-free distributions in networks and connects these to information maximization principles.

Findings

Scale-free distributions maximize information in network models.

The maximum entropy approach predicts network properties consistent with metabolic data.

Finite-fraction node suppression is linked to scale-free node distributions.

Abstract

Complex networks are mapped to a model of boxes and balls where the balls are distinguishable. It is shown that the scale-free size distribution of boxes maximizes the information associated with the boxes provided configurations including boxes containing a finite fraction of the total amount of balls are excluded. It is conjectured that for a connected network with only links between different nodes, the nodes with a finite fraction of links are effectively suppressed. It is hence suggested that for such networks the scale-free node-size distribution maximizes the information encoded on the nodes. The noise associated with the size distributions is also obtained from a maximum entropy principle. Finally explicit predictions from our least bias approach are found to be born out by metabolic networks.