The principle1 that ‘popularity is attractive’ underlies preferential attachment2, 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 laws3, 4, as observed in many real networks5, 6. Preferential attachment has been directly validated for some real networks (including the Internet7, 8), and can be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks or duplication9, 10, 11, 12, 13, 14, 15, 16. Here we show that popularity is just one dimension of attractiveness; another dimension is similarity17, 18, 19, 20, 21, 22, 23, 24. We develop a framework in which new connections optimize certain trade-offs 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 large-scale 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.
['Fragkiskos Papadopoulos', 'Maksim Kitsak', 'M. Ángeles Serrano', 'Marián Boguñá', 'Dmitri V. Krioukov']
Popularity versus Similarity in Growing Networks