Growth and Optimality in Network Evolution

TL;DR

This paper studies the evolution of networks driven by random node addition and pathlength optimization, revealing complex structures with power-law degree distributions, clustering, hierarchy, and degree mixing.

Contribution

It introduces a combined model of random assembly and optimization processes, showing how their interaction leads to complex network properties.

Findings

Networks exhibit power-law degree distributions.

Presence of non-trivial clustering and hierarchical organization.

Networks display interesting degree mixing patterns.

Abstract

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected old nodes. In between node additions, the network is rewired to minimize its pathlength. For timescales, at which neither the assembly nor the optimization processes are dominant, we find a rich variety of complex networks with power law tails in the degree distributions. These networks also exhibit non-trivial clustering, a hierarchical organization and interesting degree mixing patterns.