The spectrum of degree correlations: topological diversity of networks with a given degree sequence

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few years, many network metrics have been proposed to illuminate the network topology. Since these network metrics derive from a wide range of studies, a systematic study is required to investigate the correlations between them. The present paper investigates the correlations between some network metrics for an ensemble of graphs where the degree sequence (set of degrees) is fixed. We show that networks with the same power-law degree distribution exhibit significant differences in their topological features, as well as in responses to damages. These results suggest that only the degree distribution is not enough to classify various networks