Characterization of complex networks: A survey of measurements

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.

Generalized walks-based centrality measures for complex biological networks

“…Complex networks are also valuable in representing ecological systems, such as in the case of food webs (Jordán and Scheuring, 2004). In both contexts the use of graph theoretic invariants to characterize the local and global topology of these networks is of tremendous importance for extracting useful biological information from such networks (Costa et al, 2007;Jordán et al, 2006Jordán et al, , 2007.…”

“…Among the graph theoretic invariants characterizing biological networks, centrality indices ranking the relevance of nodes in the network have received great attention in recent years (Costa et al, 2007;Jordán et al, 2007;Junker et al, 2006). In general the notion of node centrality comes from its use in social networks (Chapter 5 in Wasserman and Faust, 1994).…”

Link prediction in complex networks: A survey

“…Figure 1 shows an example of how to calculate the AUC and Precision. In this simple graph, there are five nodes, seven existent links and three nonexistent links ((1, 2), (1,4) and (3,4) (1,4) and (4,5). Clearly, the former is wrong while the latter is right, and thus the Precision equals 0.5.…”

“…Hence we can not easily know which factor(s) leads to the scale-free property of a real network, and in fact there can be so many models competing for the final explanation of a given real network. It is very hard to evaluate different models by comparing their resulted networks with the target network, since there are too many metrics for topological features [5]. As mentioned in Section 1, there are many models about the topology of the Internet, some more accurately reproduce the degree distribution and the disassortative mixing pattern (e.g., see Ref.…”

“…The study of complex networks has therefore become a common focus of many branches of science. Great efforts have been made to understand the evolution of networks [1,2], the relations between topologies and functions [3,4], and the network characteristics [5]. An important scientific issue relevant to network analysis is the so-called information retrieval [6,7], which aims at finding material of an unstructured nature that satisfies an information need from large collections [8].…”