Characterization of complex networks: A survey of measurements

TL;DR

This survey reviews various measurements used to characterize complex networks, discussing their applications, correlations, and analysis techniques to aid in network analysis and classification.

Contribution

It provides a comprehensive overview of measurements for complex network characterization, including their applications, correlations, and analysis methods.

Findings

Analysis of measurement correlations

Discussion on network trajectory representation

Use of multivariate statistics for feature selection

Abstract

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.