A formal treatment of generalized preferential attachment and its empirical validation

¹  Boğaziçi University, Department of Computer Engineering - P.K. 2 TR-34342 Bebek, Istanbul, Turkey
²  Istanbul Technical University, Department of Computer Engineering - Ayazağa Kampüsü TR-34469, Istanbul, Turkey

Received: 3 December 2006
Accepted: 8 May 2007

Abstract

Generalized preferential attachment is defined as the tendency of a vertex to acquire new links in the future with respect to a particular vertex property. Understanding which properties influence the link acquisition tendency (LAT) gives us a predictive power to estimate the future growth of network and insight about the actual dynamics governing the complex networks. In this study, we explore the effect of age and degree on LAT by analyzing data collected from a new complex-network growth dataset. We found that LAT and degree of a vertex are linearly correlated in accordance with previous studies. Interestingly, the relation between LAT and age of a vertex is found to be in conflict with the known models of network growth. We identified three different periods in the network's lifetime where the relation between age and LAT is strongly positive, almost stationary and negative correspondingly.