Characterization of complex networks: A survey of measurements

Abstract

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