Connectivity correlations in three topological spaces of urban bus-transport networks in China

In this paper, an empirical investigation is presented, which focuses on unveiling the universality of connectivity correlations in three spaces （the route space, the stop geographical space and bus-transferring space） of urban bustransport networks （BTNs） in four major cities of China. The underlying features of the connectivity correlations are shown in two statistical ways. One is the correlation between the （weighted） average degree of all the nearest neighbouring vertices with degree k, （Knn^w,（k）） Knn（k）, and k, and the other is the correlations between the assortativity coefficient r and, respectively, the network size N, the network diameter D, the averaged clustering coefficient C, and the averaged distance （l）. The obtained results show qualitatively the same connectivity correlations of all the considered cities under all the three spaces.     

Heterogeneity of Some Cooperation/Competition Properties

We show that the heterogeneity index, which was proposed by Hu and Wang [Physica A 387 （2008） 3769], can be used to describe the disparity of the cooperation sharing or competition gain distributions, which is very important for understanding the dynamics of a cooperation/competition system. An analytical relation between the distribution parameters and the heterogeneity index is derived, which is in good agreement with the empirical results. Our theoretical and empirical analyses also show that the relation between the distribution parameters can be analytically derived from the so-called Zhang-Chang model [Physica A 360 （2006） 599; 383 （2007） 687）. This strongly recommends a possibility to create a general dynamic cooperation/competition model.