Research on Some Bus Transport Networks with Random Overlapping Clique Structure

On the basis of investigating the statistical data of bus transport networks of three big cities in China,wepropose that each bus route is a clique(maximal complete subgraph)and a bus transport network(BTN)consists of alot of cliques,which intensively connect and overlap with each other.We study the network properties,which includethe degree distribution,multiple edges' overlapping time distribution,distribution of the overlap size between any twooverlapping cliques,distribution of the number of cliques that a node belongs to.Naturally,the cliques also constitute anetwork,with the overlapping nodes being their multiple links.We also research its network properties such as degreedistribution,clustering,average path length,and so on.We propose that a BTN has the properties of random cliqueincrement and random overlapping clique,at the same time,a BTN is a small-world network with highly clique-clusteredand highly clique-overlapped.Finally,we introduce a BTN evolution model,whose simulation results agree well withthe statistical laws that emerge in real BTNs.

An evolutionary model of urban bus transport network based on B-space

In this paper, an evolutionary model of bus transport network in B-space is developed. It includes the effect of the overlapping ratio of new route on network performance and overcomes the disadvantage, i.e. lack of economic consideration, in the evolutionary bus transport network model in P-space proposed by Chen et al （2007）. The degree distribution functions are derived by using the mean-field method and the master equation method, separately. The relationship between the new stop ratio of a route, λ, and the error in exponential of degree distribution function from the mean-field method is developed as ASlope= λ/（1 -λ） ＋ ln（1-λ）. Finally, the bus transport networks of Hangzhou and Nanjing are simulated by using this model, and the results show that some characteristic index values of the simulated networks are closer to the empirical data than those from Chen＇s model.

Research on Community Structure in Bus Transport Networks

We abstract the bus transport networks(BTNs)to two kinds of complex networks with space L and spaceP methods respectively.Using improved community detecting algorithm(PKM agglomerative algorithm),we analyzethe community property of two kinds of BTNs graphs.The results show that the BTNs graph described with space Lmethod have obvious community property,but the other kind of BTNs graph described with space P method have not.The reason is that the BTNs graph described with space P method have the intense overlapping community propertyand general community division algorithms can not identify this kind of community structure.To overcome this problem,we propose a novel community structure called N-depth community and present a corresponding community detectingalgorithm,which can detect overlapping community.Applying the novel community structure and detecting algorithmto a BTN evolution model described with space P,whose network property agrees well with real BTNs',we get obviouscommunity property.

Empirical investigation of topological and weighted properties of a bus transport network from China

Many bus transport networks （BTNs） have evolved into directed networks. A new representation model for BTNs is proposed, called directed-space P. The bus transport network of Harbin （BTN-H） is described as a directed and weighted complex network by the proposed representation model and by giving each node weights. The topological and weighted properties are revealed in detail. In-degree and out-degree distributions, in-weight and out-weight distributions are presented as an exponential law, respectively. There is a strong relation between in-weight and in-degree （also between out-weight and out-degree）, which can be fitted by a power function. Degree-degree and weight-weight correlations are investigated to reveal that BTN-H has a disassortative behavior as the nodes have relatively high degree （or weight）. The disparity distributions of out-degree and in-degree follow an approximate power-law. Besides, the node degree shows a near linear increase with the number of routes that connect to the corresponding station. These properties revealed in this paper can help public transport planners to analyze the status quo of the BTN in nature.

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

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

A novel weighted evolving network model based on clique overlapping growth

A novel weighted evolving network model based on the clique overlapping growth was proposed.The model shows different network characteristics under two different selection mechanisms that are preferential selection and random selection.On the basis of mean-field theory,this model under the two different selection mechanisms was analyzed.The analytic equations of distributions of the number of cliques that a vertex joins and the vertex strength of the model were given.It is proved that both distributions follow the scale-free power-law distribution in preferential selection mechanism and the exponential distribution in random selection mechanism,respectively.The analytic expressions of exponents of corresponding distributions were obtained.The agreement between the simulations and analytical results indicates the validity of the theoretical analysis.Finally,three real transport bus networks(BTNs) of Beijing,Shanghai and Hangzhou in China were studied.By analyzing their network properties,it is discovered that these real BTNs belong to a kind of weighted evolving network model with clique overlapping growth and random selection mechanism that was proposed in this context.