Homophyly Networks -- A Structural Theory of Networks

TL;DR

This paper introduces a structural theory of networks based on homophyly, explaining community structures as a universal phenomenon driven by shared features among nodes, supported by a new model satisfying multiple principles.

Contribution

It proposes the homophyly model as a novel mechanism for community structures, establishing a comprehensive structural theory of networks.

Findings

Networks exhibit universal community structures.

Homophyly explains the mechanism behind community formation.

Power law and small world properties do not hinder community structures.

Abstract

A grand challenge in network science is apparently the missing of a structural theory of networks. The authors have showed that the existence of community structures is a universal phenomenon in real networks, and that neither randomness nor preferential attachment is a mechanism of community structures of network \footnote{A. Li, J. Li, and Y. Pan, Community structures are definable in networks, and universal in the real world, To appear.}. This poses a fundamental question: What are the mechanisms of community structures of real networks? Here we found that homophyly is the mechanism of community structures and a structural theory of networks. We proposed a homophyly model. It was shown that networks of our model satisfy a series of new topological, probabilistic and combinatorial principles, including a fundamental principle, a community structure principle, a degree priority principle, a widths principle, an inclusion and infection principle, a king node principle, and a predicting principle etc, leading to a structural theory of networks. Our model demonstrates that homophyly is the underlying mechanism of community structures of networks, that nodes of the same community share common features, that power law and small world property are never obstacles of the existence of community structures in networks, and that community structures are definable in networks.