Abstract
Preferential attachment is a stochastic process that has been proposed to explain certain topological features characteristic of complex networks from diverse domains. The systematic investigation of preferential attachment is an important area of research in network science, not only for the theoretical matter of verifying whether this hypothesized process is operative in real-world networks, but also for the practical insights that follow from knowledge of its functional form. Here we describe a maximum likelihood based estimation method for the measurement of preferential attachment in temporal complex networks. We call the method PAFit, and implement it in an R package of the same name. PAFit constitutes an advance over previous methods primarily because we based it on a nonparametric statistical framework that enables attachment kernel estimation free of any assumptions about its functional form. We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations. What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form. Independent of our main work, we provide a correction to a consequential error in Newman’s original method which had evidently gone unnoticed since its publication over a decade ago.
Highlights
The de facto maxim of network science is ‘all systems are networks.’ For those who are wellacquainted with this network view of reality, recognizing the network nature of virtually any real-world system borders on reflexive
To be plain: we focus on understanding the extent to which a process know as preferential attachment (PA) explains the emergence of those heavy-tailed degree distributions, best exemplified by power-laws, that are commonly observed in temporal complex networks across nature, society, and technology [3]
We proposed a statistically sound method, called PAFit, for estimating the attachment kernel Ak in temporal networks
Summary
The de facto maxim of network science is ‘all systems are networks.’ For those who are wellacquainted with this network view of reality, recognizing the network nature of virtually any real-world system borders on reflexive. The de facto maxim of network science is ‘all systems are networks.’. For those who are wellacquainted with this network view of reality, recognizing the network nature of virtually any real-world system borders on reflexive. Network scientists are not interested in studying just any old networks. Network scientists habitually confine themselves to the study of complex networks, that is, large-scale networks with emergent topological features that are not found to occur in simple networks [1]. Complex network research turns more or less on the study of two related problems: first, the modelling of dynamical processes taking place on static complex networks in a manner that makes judicious use of known topological features [2], and second, the study of how topological features emerge in temporal complex networks and PLOS ONE | DOI:10.1371/journal.pone.0137796. Complex network research turns more or less on the study of two related problems: first, the modelling of dynamical processes taking place on static complex networks in a manner that makes judicious use of known topological features [2], and second, the study of how topological features emerge in temporal complex networks and PLOS ONE | DOI:10.1371/journal.pone.0137796 September 17, 2015
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
