Popularity versus similarity in growing networks

• Published in: Nature (London) Vol. 489; no. 7417; pp. 537 - 540
• Main Authors: Papadopoulos, Fragkiskos, Kitsak, Maksim, Serrano, M. Ángeles, Boguñá, Marián, Krioukov, Dmitri
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 27.09.2012; Nature Publishing Group
• Subjects: 631/114/2408; 639/766/25; Applied sciences; Biological and medical sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; E coli; Escherichia coli - metabolism; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; Humanities and Social Sciences; Humans; Information retrieval. Graph; Internet - statistics & numerical data; letter; Metabolic Networks and Pathways; Models, Biological; Models, Theoretical; multidisciplinary; Probability; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Reproducibility of Results; Science; Science (multidisciplinary); Social interactions. Communication. Group processes; Social Networking; Social psychology; Software; Studies; Theoretical computing; Trust; Probabilistic approach; Hierarchical classification; Escherichia coli; Random walk; Social network; Dynamical system; Distributed system; Optimization; Social interaction; Preference; Technological change; Size effect; Bacteria; Large scale; Internet; Bioinformatics; Power law; Enterobacteriaceae
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/nature11459

A framework is developed in which new connections to a growing network optimize geometric trade-offs between popularity and similarity, instead of simply preferring popular nodes; this approach accurately describes the large-scale evolution of various networks. Networks driven by the liked and alike Preferential attachment is a mechanism that attempts to explain the emergence of scaling in growing networks. If new connections are preferentially established with more popular nodes in a network, then the network is scale-free. So, because 'popularity is attractive', does preferential attachment predict network evolution? This study shows that popularity is a strong force in shaping complex network structure and dynamics, but so too is similarity. The authors develop a model that increases the accuracy of network-evolution predictions by considering the trade-offs between popularity and similarity. The model accurately describes large-scale evolution of technological (Internet), social and metabolic networks, predicting the probability of new links with high precision. The principle 1 that ‘popularity is attractive’ underlies preferential attachment 2 , 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 3 , 4 , as observed in many real networks 5 , 6 . Preferential attachment has been directly validated for some real networks (including the Internet 7 , 8 ), and can be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks or duplication 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 . Here we show that popularity is just one dimension of attractiveness; another dimension is similarity 17 , 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.