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Multiplicative Attribute Graph Model of Real-World Networks (1009)
| Citations: | 46 - 4 self |
BibTeX
@MISC{Kim09multiplicativeattribute,
author = {Myunghwan Kim and Jure Leskovec},
title = {Multiplicative Attribute Graph Model of Real-World Networks},
year = {1009}
}
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Abstract
Large scale real-world 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 attribute-attribute 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 log-normal or power-law degree distribution depending on certain conditions. 1
Keyphrases
real-world network multiplicative attribute graph model social network network structure node attribute degree distribution tractable model web graph giant connected component mathematical analysis certain condition individual attribute-attribute similarity multiplicative attribute graph categorical latent attribute network model constant diameter power-law degree distribution large scale real-world network data rich set information network
