Dense and sparse vertex connectivity in networks

TL;DR

This paper introduces ItRich, an algorithm that identifies key nodes with meaningful local interactions in networks by decomposing graphs into layers of decreasing density, offering insights into community structure beyond traditional methods.

Contribution

The paper presents a novel algorithm, ItRich, for detecting influential nodes based on local interactions through graph layer decomposition, complementing existing community detection techniques.

Findings

ItRich effectively identifies key nodes in synthetic and real networks.

The method aligns well with community detection and k-core decomposition.

It provides new insights into internal community organization.

Abstract

The different approaches developed to analyze the structure of complex networks have generated a large number of studies. In the field of social networks at least, studies mainly address the detection and analysis of communities. In this paper, we challenge these approaches and focus on nodes that have meaningful local interactions able to identify the internal organization of communities or the way communities are assembled. We propose an algorithm, ItRich, to identify this type of nodes, based on the decomposition of a graph into successive, less and less dense, layers. Our method is tested on synthetic and real data sets and meshes well with other methods such as community detection or k-core decomposition.