Popularity versus Similarity in Growing Networks (1106.0286v3)

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.

• The paper introduces a dual-dimensional framework that integrates both popularity and similarity to model connection formation in growing networks.
• Simulations validate that the model replicates real network properties such as clustering coefficients and degree distributions more accurately than classical mechanisms.
• The findings provide actionable insights for advancing link prediction techniques in social, technical, and biological network applications.

Popularity versus Similarity in Growing Networks

This paper introduces a dual-dimensional framework to address the formation of connections in growing networks. It critiques the classical notion of Preferential Attachment (PA)—a mechanism that assembles networks through node popularity—and proposes an augmented model incorporating both popularity and similarity dimensions.

Theoretical Framework

The authors present a model where network growth is driven by a trade-off between node popularity and similarity. Popularity is traditionally seen as a singular attraction metric; however, this paper introduces similarity as a concurrent and influential factor. The framework theorizes that new nodes do not only connect with the most popular nodes but also with those sharing inherent similarities. This dual-metric model is represented geometrically, simplifying complex growth behaviors into interpretable distance metrics on a hyperbolic plane.

Empirical Insights and Simulations

Key to this model’s validation are simulations showing that networks generated under this dual approach closely match real-world systems. Specifically, the popularity$\times$similarity construct accurately predicts link formation probabilities with high precision, surpassing PA in networks like the Internet, social webs of trust, and biological networks. The results suggest clustering coefficients and degree distributions are effectively captured, showcasing exponents akin to actual observed values.

Model Modifications and Flexibility

The model permits several modifications to adjust clustering and degree distributions, such as varying node drift or network temperature. This flexibility inherently addresses limitations seen in the PA model, specifically offering configurations that resonate with real-world network dynamics, like assortativity and clustering.

Implications

From a practical perspective, this work presents novel approaches for link prediction, crucial in biological network analysis, social networking applications, and the optimization of technological infrastructures. The theoretical insights also bridge a gap in network science by providing a clear geometric interpretation of network evolution.

Conclusion and Outlook

The incorporation of similarity alongside popularity offers a cohesive theory that characterizes the underlying structures of evolving large-scale networks. Moving forward, this framework could inform the design of network algorithms that leverage intrinsic similarity metrics, enhancing predictive modeling in diverse domains ranging from beyond social sciences to complex biological studies. The multidimensional approach promises further explorations, especially in elucidating network topology through latent metrics unseen in traditional models.