Evolving Model for the Complex Traffic and Transportation Network Considering Self-Growth Situation

It has been approved that the scale-free feature exists in various complex networks, such as the internet, the cell or the biological networks. In order to analyze the influence of the self-growth phenomenon during the growth on the structure of traffic and transportation network, we formulated an evolving model. Based on the evolving model, we prove in mathematics that, even that the self-growth situation happened, the traffic and transportation network owns the scale-free feature due to that the node degree follows a power-law distribution. A real traffic and transportation network, China domestic airline network is tested to consolidate our conclusions. We find that the airline network has a node degree distribution equivalent to the power-law of which the estimated scaling parameter is about 3.0. Moreover the standard error of the estimated scaling parameter changes according to the self-growth probability. Our findings could provide useful information for determining the optimal structure or status of the traffic and transportation network.