Density decompositions of networks

TL;DR

This paper introduces the density decomposition, a unique topological network descriptor that partitions nodes into regions of uniform density, revealing similarities to degree distributions in real networks and differences in synthetic models.

Contribution

It presents a novel, unique density decomposition method for networks and demonstrates its relevance by comparing real and synthetic network structures.

Findings

Density distributions in real networks resemble degree distributions.

Synthetic networks show dissimilar density and degree distributions.

Density decomposition is a measurable and distinctive network feature.

Abstract

We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network has exactly one density decomposition. The number of nodes in each partition defines a density distribution which we find is measurably similar to the degree distribution of given real networks (social, internet, etc.) and measurably dissimilar in synthetic networks (preferential attachment, small world, etc.).