Multiplicative Attribute Graph Model of Real-World Networks

  • Myunghwan Kim
  • Jure Leskovec
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6516)


Large scale real-world network data such as social and information networks are ubiquitous. The study of such 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 associated with them. We present the Multiplicative Attribute Graphs (MAG) model, 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 depends on the product of individual attribute-attribute similarities. The model yields itself to mathematical analysis. 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 also show that MAG model can produce networks with either log-normal or power-law degree distributions.


social networks network model latent attribute node model 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Myunghwan Kim
    • 1
  • Jure Leskovec
    • 1
  1. 1.Stanford UniversityStanfordUSA

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