Beyond the Expanders

TL;DR

This paper explores the limitations of expander graphs in modeling social and biological networks, proposing a focus on regularity properties and spectral implications for understanding information flow.

Contribution

It introduces a new perspective on network regularity and spectral properties beyond traditional expander graph models, with implications for complex network analysis.

Findings

Spectral properties relate to regularity in network subgraphs.

Expander graphs do not fully capture information flow in social/biological networks.

Partitioning networks reveals regular behavior in subgraphs.

Abstract

Expander graphs are widely used in communication problems and construction of error correcting codes. In such graphs, information gets through very quickly. Typically, it is not true for social or biological networks, though we may find a partition of the vertices such that the induced subgraphs on them and the bipartite subgraphs between any pair of them exhibit regular behavior of information flow within or between the subsets. Implications between spectral and regularity properties are discussed.