Concentric Characterization and Classification of Complex Network Nodes: Theory and Application to Institutional Collaboration

TL;DR

This paper introduces a method using concentric measurements and clustering to classify nodes in complex networks, revealing functional groups and patterns in institutional collaboration networks, with insights into their scale-free properties.

Contribution

It demonstrates the effectiveness of concentric measurements combined with clustering to identify functional groups in real-world networks, differing from traditional local topology approaches.

Findings

Identified distinct functional groups in an institutional collaboration network.

Revealed scale-free properties and diverse authorship patterns.

Found a uniform distribution of hubs across levels, contrasting with theoretical models.

Abstract

Differently from theoretical scale-free networks, most of real networks present multi-scale behavior with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes in a complex network has relied on local measurements of the topology/connectivity around each node, valuable information about node functionality can be obtained by Concentric (or Hierarchical) Measurements. In this paper we explore the possibility of using a set of Concentric Measurements and agglomerative clustering methods in order to obtain a set of functional groups of nodes. Concentric clustering coefficient and convergence ratio are chosen as segregation parameters for the analysis of a institutional collaboration network including various known communities (departments of the University of S\~ao Paulo). A dendogram is obtained and the results are analyzed and discussed. Among the interesting obtained findings, we emphasize the scale-free nature of the obtained network, as well as the identification of different patterns of authorship emerging from different areas (e.g. human and exact sciences). Another interesting result concerns the relatively uniform distribution of hubs along the concentric levels, contrariwise to the non-uniform pattern found in theoretical scale free networks such as the BA model.