Node Degree Dynamics in Complex Networks Generated in Accordance with a Modification of the Triadic Closure Model

Abstract

AbstractThe triadic closure model attempts to reflect the well-known fact that many real-world networks have a much higher likelihood of a link between a pair of nodes with a common neighbor than in the random null model. The effect is especially evident in social networks and is also widely present in cooperation networks in the field of knowledge, citation and research, and many others. It should be noted that in the triadic closure model proposed by P. Holme and B.J. Kim, at the triad formation step, the new link is attached to any random neighbor (which is chosen evenly) of the node selected in the previous step (which is chosen using the preferential attachment mechanism). However, in many real-world complex networks, the second link is also usually selected using the preferential attachment mechanism. In this paper, we propose to make adjustments to the triadic closure model for the case when the nodes are selected using the preferential attachment mechanism at the triad formation step. We empirically investigate the dynamics of the mean value of node degree in the networks generated by this model and show that it follows a power law.KeywordsComplex networksSocial networksPreferential attachmentTriadic closureHigh clusteringGrowth model