Abstract :
In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment (GPA) which has two new properties; first, it encapsulates both the topological and weight aspects of a network, which makes it is neither entirely degree preferential nor entirely weight preferential. Second, it can tell us not only the chance that each already-existing vertex being connected but also how much weight each new edge has. The GPA can generate four power-law distributions, besides the three for vertex degrees, vertex strengths, and edge weights, it yields a new power-law distribution for the subgraph degrees.
