Popularity versus similarity in growing networks
Abstract
The principle that `popularity is attractive' underlies preferential attachment, which is a common explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections possessed by nodes follows power laws, as observed in many real networks. Preferential attachment has been directly validated for some real networks (including the Internet), and can be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks or duplication. Here we show that popularity is just one dimension of attractiveness; another dimension is similarity. We develop a framework in which new connections optimize certain tradeoffs between popularity and similarity, instead of simply preferring popular nodes. The framework has a geometric interpretation in which popularity preference emerges from local optimization. As opposed to preferential attachment, our optimization framework accurately describes the largescale evolution of technological (the Internet), social (trust relationships between people) and biological (Escherichia coli metabolic) networks, predicting the probability of new links with high precision. The framework that we have developed can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon.
 Publication:

Nature
 Pub Date:
 September 2012
 DOI:
 10.1038/nature11459
 arXiv:
 arXiv:1106.0286
 Bibcode:
 2012Natur.489..537P
 Keywords:

 Physics  Physics and Society;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Networking and Internet Architecture;
 Computer Science  Social and Information Networks
 EPrint:
 Nature, v.489, p.537, 2012