The topological relationship between the large-scale attributes and local interaction patterns of complex networks

TL;DR

This paper explores how the large-scale topology of complex networks influences local interaction patterns, revealing a mutual relationship and identifying two classes of subgraphs with distinct clustering behaviors.

Contribution

It demonstrates that global network structure and local subgraph patterns are mutually predictive and introduces a topological framework distinguishing two subgraph classes.

Findings

Two classes of subgraphs identified: Type I and Type II.

Type I subgraphs are abundant and form clusters.

Type II subgraphs are rare and do not cluster.

Abstract

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.