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Multiplicative Attribute Graph Model of RealWorld Networks
, 1009
"... Large scale realworld network data, such as social networks, Internet and Web graphs, are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, especially in social networks, nodes have a rich set ..."
Abstract

Cited by 45 (4 self)
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Large scale realworld network data, such as social networks, Internet and Web graphs, are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, especially in social networks, nodes have a rich set of attributes (e.g., age, gender) associated with them. However, many existing network models focus on modeling the network structure while ignoring the features of the nodes. Here we present a model that we refer to as the Multiplicative Attribute Graphs (MAG), which naturally captures the interactions between the network structure and node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes then depends on the product of individual attributeattribute similarities. This model yields itself to mathematical analysis and we derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to graphs with a constant diameter. We analyze the degree distribution to show that the model can produce networks with either lognormal or powerlaw degree distribution depending on certain conditions. 1