Popularity versus Similarity in Growing Networks

TL;DR

This paper introduces a framework that models network growth based on a trade-off between popularity and similarity, offering a more accurate description of how various real-world networks evolve and form new connections.

Contribution

It presents a novel optimization-based framework that incorporates both popularity and similarity, providing a geometric interpretation and outperforming traditional preferential attachment models.

Findings

Accurately predicts link formation in technological, social, and biological networks.

Offers a geometric interpretation of network growth.

Demonstrates superiority over preferential attachment in modeling real networks.

Abstract

Popularity is attractive -- this is the formula underlying preferential attachment, a popular 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 that nodes have follows power laws observed in many real networks. Preferential attachment has been directly validated for some real networks, including the Internet. Preferential attachment can also 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 where new connections, instead of preferring popular nodes, optimize certain trade-offs between popularity and similarity. The framework admits a geometric interpretation, in which popularity preference emerges from local optimization. As opposed to preferential attachment, the optimization framework accurately describes large-scale evolution of technological (Internet), social (web of trust), and biological (E.coli metabolic) networks, predicting the probability of new links in them with a remarkable precision. The developed framework can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon.