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 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.

Field experiments of success-breeds-success dynamics

“…For instance, although some scholars have taken the extreme variance of success distributions as a tell-tale sign of cumulative advantage (8,11,16,20), critics have pointed out that various other generative mechanisms, such as the existence of a convex correspondence between fitness and success (21,22), can generate the same empirical regularities (17,(23)(24)(25)(26)(27)(28). Further, in longitudinal records of success, unobserved dimensions of fitness generate apparent bias toward past winners (3,4,12,15).…”

Correlation Dimension of Complex Networks

“…The discovery of the real architecture of interactions of many systems studied under the former disciplines [2-4] changed the usual mean-field way to tackle problems arising in sociology, biology, epidemiology and technology among others [5]. Furthermore, the blossom of the network theoretical machinery [6], has provided a forefront framework to interpret the relations encoded in large datasets of diverse nature and fostered the application of new techniques, such as community detection algorithms [7], to coarse-grain the complex and hierarchical landscape of interactions of real-world systems.Recently, geometrical concepts have been exploited to describe and classify the structure of complex networks beyond purely topological aspects [8][9][10][11]. In particular, the box-counting technique, widely used for estimating the capacity dimension D 0 of an object, has been recently extended, as a box-covering algorithm, to characterize the dimensionality of complex networks [11][12][13][14].…”

“…Recently, geometrical concepts have been exploited to describe and classify the structure of complex networks beyond purely topological aspects [8][9][10][11]. In particular, the box-counting technique, widely used for estimating the capacity dimension D 0 of an object, has been recently extended, as a box-covering algorithm, to characterize the dimensionality of complex networks [11][12][13][14].…”

Newton’s Gravitational Law for Link Prediction in Social Networks

“…In the context of social networks it has been established that link prediction could mainly be facilitated by utilising two kinds of information in the network: popularity and similarity [37]. Our approach supports this as a special case, where popularity acts as mass and inverse of similarity as distance.…”