Rethinking Preferential Attachment Scheme: Degree Centrality versus Closeness Centrality

초록

Construction of realistic dynamic complex networks has become increasingly important. One of the more widely known approaches, Barabasi and Albert’s “scale-free” network (BA network), has been generated under the assumption that new actors make ties with high degree actors. Unfortunately, degree, as a preferential attachment scheme, is limited to a local property of network structure, which social network theory has pointed out for a long time. In order to complement this shortcoming of degree preferential attachment, this paper not only introduces closeness preferential attachment, but also compares the relationships between the degree and closeness centrality in three different types of networks: random network, degree preferential attachment network, and closeness preferential attachment network. We show that a high degree is not a necessary condition for an actor to have high closeness. Degree preferential attachment network and sparse random network have relatively small correlation between degree and closeness centrality. Also, the simulation of closeness preferential attachment network suggests that individuals’ efforts to increase their own closeness will lead to inefficiency in the whole network.