Modeling Clustered Scale-free Networks by Applying Various Preferential Attachment Patterns

Abstract

Preferential attachment phenomenon is a key factorproviding scale-free behavior in complex networks. In this study, we introducedvarious preferential attachment patterns applied in a growing Barabasi-Albertnetwork, denoted by a factor α. We first generated networks under constantpreferential attachment levels from 0 to 2, where 1 stands for linearpreferential attachment. Then we performed network simulations under uniformlydistributed random α condition, within the interval [0,2]. Although mean α is 1for this setup, generated networks displayed greater clustering together withlower modularity and separation values compared to the setup with α=1. We alsoperformed similar network generation procedures with various distributionfunctions applied for α, each resulting random levels of preferentialattachment. We achieved networks with power-law consistent degree distributionswith γ coefficients between 2 and 3, together with improved clusteringcoefficients up to ~0.3. As a result, scale-free network topologies featuringgreater clustering levels compared to pure Barabasi-Albert model are achieved.