The Irreducible Spine(s) of Undirected Networks

TL;DR

This paper introduces the concept of a unique irreducible spine in undirected networks, characterized by chordless cycles, which captures the network's connectivity structure and centrality, providing a signature for network identification.

Contribution

It defines the irreducible spine of undirected graphs using chordless cycles, linking it to network centrality and proposing a cycle-based signature for network characterization.

Findings

The irreducible spine effectively contains the network's center.

Cycle counts create a distinctive network signature.

Performance analysis demonstrates the method's applicability.

Abstract

Using closure concepts, we show that within every undirected network, or graph, there is a unique irreducible subgraph which we call its "spine". The chordless cycles which comprise this irreducible core effectively characterize the connectivity structure of the network as a whole. In particular, it is shown that the center of the network, whether defined by distance or betweenness centrality, is effectively contained in this spine. By counting the number of cycles of length 3 <= k <= max_length, we can also create a kind of signature that can be used to identify the network. Performance is analyzed, and the concepts we develop are illurstrated by means of a relatively small running sample network of about 400 nodes.