Modelling weighted networks using connection count

Abstract

Weight-driven and degree-driven evolutionary models for weighted networks are proposed, with a distance-dependent mechanism to increase the clustering coefficient. Compared with the well-known BA model there are two generalizations. Firstly, introducing connection count and converting it into edge weight, both new and old vertices can attempt to build up connections. When a new edge is inserted between already connected nodes, the connection count (and thereby the weight) of the corresponding link is increased. Secondly, the distribution of local path distance is also used as a reference in the preferential attachment. The models show some interesting results including scale-free distributions on degree, vertex weight and edge weight. Even the pure distance-dependent preferential attachment model shows all these typical behaviours and a high cluster coefficient. The concepts of reconnecting and converting count as weight are not new and have been used in empirical studies of weighted networks but are first used to model weighted networks.