Emergence of scaling in random networks

TL;DR

This paper explains how many large, complex networks naturally develop a scale-free structure through simple, universal growth mechanisms involving preferential attachment and continuous expansion.

Contribution

It introduces a model demonstrating that scale-free networks emerge from generic growth rules, highlighting the self-organizing principles behind complex network topologies.

Findings

Networks follow a power-law degree distribution

Preferential attachment explains the emergence of hubs

Model reproduces observed network structures

Abstract

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.