Unevenness of Loop Location in Complex Networks

TL;DR

This paper investigates the uneven distribution of loops in complex networks, revealing rich loop cores in real networks and proposing an index to measure loop unevenness, which enhances understanding of network structure.

Contribution

It introduces a node removing process to analyze loop distribution and presents a new index to quantify loop unevenness in complex networks.

Findings

Rich loop cores exist in neural and food web networks.

Loop unevenness can be effectively quantified.

Real networks have fewer short loops than random models.

Abstract

The loop structure plays an important role in many aspects of complex networks and attracts much attention. Among the previous works, Bianconi et al find that real networks often have fewer short loops as compared to random models. In this paper, we focus on the uneven location of loops which makes some parts of the network rich while some other parts sparse in loops. We propose a node removing process to analyze the unevenness and find rich loop cores can exist in many real networks such as neural networks and food web networks. Finally, an index is presented to quantify the unevenness of loop location in complex networks.