Detection of network inhomogeneity by total neighbor degree

TL;DR

This paper introduces a method to detect inhomogeneity in networks by analyzing the correlation between node degrees and their neighbors' total degrees, demonstrated on models and real-world networks.

Contribution

It extends the Aboav-Weaire law for multi-partition networks and applies total neighbor degree analysis to identify inhomogeneity in various network types.

Findings

Separable clustering indicates inhomogeneity in networks.

Method successfully detects inhomogeneity in real bipartite networks.

Identifies interesting node groups in semantic and WWW networks.

Abstract

Inhomogeneity in networks can be detected by the analysis of the correlation of the total degree of nearest neighbors. This is illustrated by two models. The first one is a random multi-partitions network that the Aboav Weaire law, which predicts the linear relationship between the degree of node and the total degree of nearest neighbor, is being extended. The second one is a preferential attachment network with two partitions which shows scale free properties with power tail $\gamma$ within the range $2<\gamma\le3$. By plotting the total degree of neighbor verses the degree of each node in the networks, the scattered plot shows separable clustering as evidence for inhomogeneity in networks. The effectiveness of this new tool for the detection of inhomogeneity is demonstrated in real bipartite networks. By using this method, some interesting group of nodes of semantic and WWW networks have been found.