  Large scale real-world network data such as social and information networks
are ubiquitous. The study of such social and information networks seeks to find
patterns and explain their emergence through tractable models. In most
networks, and especially in social networks, nodes have a rich set of
attributes (e.g., age, gender) associated with them.
  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 the 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
attribute-attribute affinities. The 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 networks with
a constant diameter. We analyze the degree distribution to show that MAG model
can produce networks with either log-normal or power-law degree distributions
depending on certain conditions.
