Mechanism for linear preferential attachment in growing networks

TL;DR

This paper demonstrates that linear preferential attachment naturally arises in sparse growing networks by maximizing entropy, providing theoretical support for its widespread use in network modeling and offering methods to compute degree correlations and clustering.

Contribution

It offers a theoretical foundation for linear preferential attachment as a maximal entropy principle in sparse networks and develops a method to calculate degree correlation and clustering.

Findings

Linear preferential attachment maximizes entropy in sparse networks.

Supports the use of linear preferential attachment in real-world network models.

Provides a method to compute degree correlation and clustering in sparse networks.

Abstract

The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse growing networks. This provides theoretical evidence in support of the linear preferential attachment widely exists in real networks and adopted as a crucial assumption in growing network models. Besides, in the sparse limit, we develop a method to calculate the degree correlation and clustering coefficient in our ensemble model, which is suitable for all kinds of sparse networks including the BA model, proposed by Barabasi and Albert.