On the relationships between topological measures in real-world networks

Over the past several years, a number of measures 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 measures are either fully related to other topological measures or that they are significantly limited in the range of their possible values. Second, we observe that subsets of measures are highly correlated, indicating redundancy among them. Our study thus suggests that the set of commonly used measures 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 measures that would serve in future topological studies of complex networks.