一道高考题引出圆锥曲线的一个性质

认真研读天津2004年高考理科卷第22题：     

The effects of degree correlations on network topologies and robustness

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