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On the relationships between topological metrics in real-world networks

Over the past several years, a number of metrics have been introduced to characterize the topology of complex networks. We perform a statistical analysis of real data sets, representing the topology of different real-world networks. First, we show that some metrics are either fully related to other topological metrics or that they are significantly limited in the range of their possible values. Second, we observe that subsets of metrics are highly correlated, indicating redundancy among them. Our study thus suggests that the set of commonly used metrics is too extensive to concisely characterize the topology of complex networks. It also provides an important basis for classification and unification of a definite set of metrics that would serve in future topological studies of complex networks.