A Statistical Physics Perspective on Web Growth

TL;DR

This paper applies statistical physics methods to analyze the growth and structure of web-like networks, revealing different behaviors based on growth rules and matching real-world web data.

Contribution

It introduces a comprehensive statistical physics framework to model web growth, including degree distributions, correlations, and directed networks, aligning with empirical web data.

Findings

Degree distribution varies with gamma parameter, showing different behaviors.

Power-law degree distributions match observed web data.

Global network properties and sub-network growth are characterized.

Abstract

Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the world-wide web. We first determine the degree distribution of a growing network in which nodes are introduced one at a time and attach to an earlier node of degree k with rate A_ksim k^gamma. Very different behaviors arise for gamma<1, gamma=1, and gamma>1. We also analyze the degree distribution of a heterogeneous network, the joint age-degree distribution, the correlation between degrees of neighboring nodes, as well as global network properties. An extension to directed networks is then presented. By tuning model parameters to reasonable values, we obtain distinct power-law forms for the in-degree and out-degree distributions with exponents that are in good agreement with current data for the web. Finally, a general growth process with independent introduction of nodes and links is investigated. This leads to independently growing sub-networks that may coalesce with other sub-networks. General results for both the size distribution of sub-networks and the degree distribution are obtained.