What are the Best Hierarchical Descriptors for Complex Networks?

TL;DR

This paper reviews hierarchical measurements of complex networks and uses feature selection to identify the most effective descriptors for distinguishing between four theoretical network models.

Contribution

It systematically evaluates the importance of various hierarchical network measurements for model discrimination, highlighting the most effective features.

Findings

Hierarchical clustering coefficients are highly effective for model discrimination.

Traditional measures like average shortest path length contribute little to model separation.

A combination of selected measurements can well-separate different network models.

Abstract

This work reviews several hierarchical measurements of the topology of complex networks and then applies feature selection concepts and methods in order to quantify the relative importance of each measurement with respect to the discrimination between four representative theoretical network models, namely Erd\"{o}s-R\'enyi, Barab\'asi-Albert, Watts-Strogatz as well as a geographical type of network. The obtained results confirmed that the four models can be well-separated by using a combination of measurements. In addition, the relative contribution of each considered feature for the overall discrimination of the models was quantified in terms of the respective weights in the canonical projection into two dimensions, with the traditional clustering coefficient, hierarchical clustering coefficient and neighborhood clustering coefficient resulting particularly effective. Interestingly, the average shortest path length and hierarchical node degrees contributed little for the separation of the four network models.