2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124059In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment 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 generalized preferential attachment can generate four power-law distributions, besides the three for vertex degrees, vertex strengths, and edge weights, it yield a new power-law distribution for the subgraph degrees.17 pages, 4 figures, final version, Physica A, 377, 709, 2007Physics and SocietyDisordered Systems and Neural NetworksData Analysis, Statistics and Probabilitytext