The effects of degree correlations on network topologies and robustness

Complex networks have been applied to model numerous interactivenonlinear systems in the real world. Knowledge about network topologyis crucial to an understanding of the function, performance andevolution of complex systems. In the last few years, many networkmetrics and models have been proposed to investigate the networktopology, dynamics and evolution. Since these network metrics andmodels are derived from a wide range of studies, a systematic studyis required to investigate the correlations among them. The presentpaper explores the effect of degree correlation on the other networkmetrics through studying an ensemble of graphs where the degreesequence (set of degrees) is fixed. We show that to some extent, thecharacteristic path length, clustering coefficient, modular extentand robustness of networks are directly influenced by the degreecorrelation.