Abstract
Many real-world systems are profitably described as complex networks that grow over time. Preferential attachment and node fitness are two simple growth mechanisms that not only explain certain structural properties commonly observed in real-world systems, but are also tied to a number of applications in modeling and inference. While there are statistical packages for estimating various parametric forms of the preferential attachment function, there is no such package implementing non-parametric estimation procedures. The non-parametric approach to the estimation of the preferential attachment function allows for comparatively finer-grained investigations of the `rich-get-richer' phenomenon that could lead to novel insights in the search to explain certain nonstandard structural properties observed in real-world networks. This paper introduces the R package PAFit, which implements non-parametric procedures for estimating the preferential attachment function and node fitnesses in a growing network, as well as a number of functions for generating complex networks from these two mechanisms. The main computational part of the package is implemented in C++ with OpenMP to ensure scalability to large-scale networks. We first introduce the main functionalities of PAFit through simulated examples, and then use the package to analyze a collaboration network between scientists in the field of complex networks. The results indicate the joint presence of `rich-get-richer' and `fit-get-richer' phenomena in the collaboration network. The estimated attachment function is observed to be near-linear, which we interpret as meaning that the chance an author gets a new collaborator is proportional to their current number of collaborators. Furthermore, the estimated author fitnesses reveal a host of familiar faces from the complex networks community among the field's topmost fittest network scientists.
Highlights
IntroductionSince the end of the last century, complex networks have been increasingly used in modeling many temporal relations found in diverse fields
Since the end of the last century, complex networks have been increasingly used in modeling many temporal relations found in diverse fields (Dorogovtsev and Mendes 2003; Caldarelli2007; Newman 2010)
This paper introduces the R package PAFit (Pham, Sheridan, and Shimodaira 2020), which is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project
Summary
Since the end of the last century, complex networks have been increasingly used in modeling many temporal relations found in diverse fields This observation prompted network scientists to search for new modeling ingredients capable of explaining heavy-tailed degree distributions What they found is that temporal complex network models incorporating growth mechanisms offer a powerful modeling framework for achieving this end. Based on the functional forms of Ak and ηi , we can test for the presence of one and/or the other of the “rich-get-richer” and “fit-getricher” phenomena in a temporal network (Pham, Sheridan, and Shimodaira 2016) These two mechanisms have been advanced to explain another phenomenon called the “generalized friendship paradox” (Feld 1991; Eom and Jo 2014; Momeni and Rabbat 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
