Hierarchical characterization of complex networks

TL;DR

This paper introduces hierarchical measurements like node degree and clustering coefficient to better characterize complex networks, revealing topological features beyond immediate neighborhoods and enabling network taxonomy.

Contribution

It extends existing hierarchical network measurements with new metrics and demonstrates their effectiveness on various network models and real-world data.

Findings

Hierarchical measurements improve network characterization.

Enhanced metrics distinguish different network types.

Hierarchical data enable node taxonomy through clustering.

Abstract

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work discusses on how the concepts of hierarchical node degree and hierarchical clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, can be used in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.