Preferential Attachment in Online Networks: Measurement and Explanations

Abstract

We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network considered. The classical preferential attachment model for networks by Barabási and Albert (1999) assumes a linear relationship between the number of neighbors of a node in a network and the probability of attachment. Although this assumption is widely made in Web Science and related fields, the underlying linearity is rarely measured. To fill this gap, this paper performs an empirical longitudinal (time-based) study on forty-seven diverse Web network datasets from seven network categories and including directed, undirected and bipartite networks. We show that contrary to the usual assumption, preferential attachment is nonlinear in the networks under consideration. Furthermore, we observe that the deviation from linearity is dependent on the type of network, giving sublinear attachment in certain types of networks, and superlinear attachment in others. Thus, we introduce the preferential attachment exponent $\beta$ as a novel numerical network measure that can be used to discriminate different types of networks. We propose explanations for the behavior of that network measure, based on the mechanisms that underly the growth of the network in question.

10 pages, 5 figures, Accepted for the WebSci'13 Conference, Paris, 2013

References in corpus (10)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Power laws, Pareto distributions and Zipf's law
• Evolution of networks
• Clustering and preferential attachment in growing networks
• Organization of Growing Random Networks
• Measuring preferential attachment for evolving networks
• Information dynamics shape the networks of Internet-mediated prostitution
• Scale-free networks as preasymptotic regimes of superlinear preferential attachment

Cited by in corpus (2)

• A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-normal In-degree Distributions
• A Preferential Attachment Model for the Stellar Initial Mass Function