A General Evolution Mechanism Model for E-Commerce Network

Scale-Free Network

One of the most important properties of real world self-organized networks is their scale-free property, including the World Wide Web (Adamic & Huberman, 2000), Internet (Faloutsos et al., 1999), market investments (Garlaschellia, et al., 2005) and so on.

A network with the scale-free property follows the power-law distribution p(k)~k^-γ, which means most nodes in the network will have a few links and a few nodes will have a large number of links (Barabasi & Albert, 1999). Here, the degree k means the number of links of a given node. The latter ones can be named hub nodes. This may result in a high dependency on the hub nodes. The most important exponent γ of the power function represents the characteristic and shape of the network topology. If the exponent γ is small, a few hubs dominate the network. As many empirical studies and numerical simulations of the network evolution have shown, the exponent γ of the node degree frequency distribution of these networks ranges between 2 and 3. The emergence of the power-law degree distribution has been traced back to two mechanisms. First, most networks grow through the addition of new nodes, that link to nodes already present in the system. Second, most real networks exhibit preferential attachment, i.e..