Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure

<正> Transport networks, such as railway networks and airport networks, are a kind of random network withcomplex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try toexplore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus TransportNetworks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for theobserved exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-fieldtheory, we analyze the BTNs model and prove that this model has the character of exponential distribution of theconnectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculateanalytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with thestatistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponentialdistribution of the connectivities, and their exponents have same order of magnitude, which show the availability of theanalytical result of this paper.