Bus transport network model with ideal n-depth clique network topology

We propose an ideal n-depth clique network model. In this model, the original network is composed of cliques (maximal complete subgraphs) that overlap with each other. The network expands continuously by the addition of new cliques. The final diameter of the network can be set in advance, namely, it is controllable. Assuming that the diameter of the network is n, the network exhibits a logistic structure with (n+1) layers. In this structure, the 0th layer represents the original network and each node of the (m)th layer (1≤m≤n) corresponds to a clique in the (m−1)th layer. In the growth process of the network, we ensure that any (m)th layer network is composed of overlapping cliques. Any node in an (m)th layer network corresponds to an m-depth community in the original network, and the diameter of an m-depth community is m. Therefore, the (n−1)th layer network will contain only one clique, the (n)th layer network will contain only one node, and the diameter of the corresponding original network is n. Then an ideal n-depth clique network will be obtained. Based on the ideal n-depth clique network model, we construct a bus transport network model with an ideal n-depth clique network topology (ICNBTN). Moreover, our study compares this model with the real bus transport network (RealBTN) of three major cities in China and a recently introduced bus transport network model (BTN) whose network properties correspond well with those of real BTNs. The network properties of the ICNBTN are much closer to those of the RealBTN than those of the BTN are. At the same time, the ICNBTN has higher clustering extent of bus routes, smaller network diameter, which corresponds to shorter maximum transfer times in a bus network, and lower average shortest path time coefficient than the BTN and the RealBTN. Therefore, the ICNBTN can achieve higher transfer efficiency for a bus transport system.