Characterization of Subgraphs Relationships and Distribution in Complex Networks

TL;DR

This paper introduces a new method for analyzing the relationships and distribution of specific subgraphs within complex networks, focusing on subgraphs sharing particular features, and demonstrates its utility across various network types.

Contribution

The paper presents a novel intermediate-level topological analysis method for characterizing non-overlapping subgraphs and their interrelationships in complex networks.

Findings

Effective in analyzing different network models and real-world networks.

Provides insights into subgraph distribution and interconnectivity.

Complements existing network analysis techniques.

Abstract

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs (connected components) and their interrelationships and distribution through the network. Though such subgraphs can be completely general, our methodology focuses the cases in which the nodes of these subgraphs share some special feature, such as being critical for the proper operation of the network. Our methodology of subgraph characterization involves two main aspects: (i) a distance histogram containing the distances calculated between all subgraphs, and (ii) a merging algorithm, developed to progressively merge the subgraphs until the whole network is covered. The latter procedure complements the distance histogram by taking into account the nodes lying between subgraphs, as well as the relevance of these nodes to the overall interconnectivity. Experiments were carried out using four types of network models and four instances of real-world networks, in order to illustrate how subgraph characterization can help complementing complex network-based studies.