Persistent Homology of Complex Networks

TL;DR

This paper introduces persistent homology as a new topological invariant to analyze complex networks, revealing how persistent features relate to network robustness and connectivity properties.

Contribution

It presents persistent homology as a novel approach for studying complex networks, linking topological features to network robustness and connectivity.

Findings

Distinct degree distributions show unique persistent topological features.

Persistent topological attributes relate to network robustness.

Analysis includes random, exponential, and scale-free networks.

Abstract

Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and presented as a parametrized version of a Betti number. Complex networks with distinct degree distributions exhibit distinct persistent topological features. Persistent toplogical attributes, shown to be related to robust quality of networks, also reflect defficiency in certain connectivity properites of networks. Random networks, networks with exponential conectivity distribution and scale-free networks were considered for homological persistency analysis.