Network Structures from Selection Principles

TL;DR

This paper analyzes optimal network topologies balancing short routes and low congestion, revealing diverse structures and phase transitions, suggesting natural topologies emerge from growth and dynamical-selection interactions.

Contribution

It introduces a framework for understanding network topologies based on selection principles, highlighting phase transitions and the emergence of natural-like structures.

Findings

Multiple distinct topologies identified

Phase transitions observed with link number variation

Natural topologies may result from growth and dynamical interactions

Abstract

We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible. Strikingly, we find a variety of distinct topologies and novel phase transitions between them on varying the number of links per node. Our results suggest that the emergence of the topologies observed in nature may arise both from growth mechanisms and the interplay of dynamical mechanisms with a selection process.