Network partition via a bound of the spectral radius

TL;DR

This paper introduces bounds on the spectral radius based on high-degree node connections, enabling network partitioning into a spectral-core that approximates leading eigenvector entries and aids in spectral radius reduction.

Contribution

It presents novel bounds on the spectral radius derived from connection densities, and a method to partition networks into a spectral-core for spectral analysis.

Findings

Spectral-core correlates with the top eigenvector entries.

Spectral-core properties depend on network assortativity.

Method effectively reduces spectral radius in real networks.

Abstract

Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this set as the spectral--core. The degree of the nodes of the subnetwork formed by the spectral--core gives an approximation to the top entries of the leading eigenvector of the whole network. We also present some numerical examples showing the dependancy of the spectral--core with the assortativity coefficient, its evaluation in several real networks and how the properties of the spectral--core can be used to reduce the spectral radius.