Large scale real-world network data such as social and information networksare ubiquitous. The study of such social and information networks seeks to findpatterns and explain their emergence through tractable models. In mostnetworks, and especially in social networks, nodes have a rich set ofattributes (e.g., age, gender) associated with them. Here we present a model that we refer to as the Multiplicative AttributeGraphs (MAG), which naturally captures the interactions between the networkstructure and the node attributes. We consider a model where each node has avector of categorical latent attributes associated with it. The probability ofan edge between a pair of nodes then depends on the product of individualattribute-attribute affinities. The model yields itself to mathematicalanalysis and we derive thresholds for the connectivity and the emergence of thegiant connected component, and show that the model gives rise to networks witha constant diameter. We analyze the degree distribution to show that MAG modelcan produce networks with either log-normal or power-law degree distributionsdepending on certain conditions.
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