Multiplicative Attribute Graph Model of Real-World Networks

TL;DR

This paper introduces the Multiplicative Attribute Graph (MAG) model that captures how node attributes influence network structure, providing analytical insights into connectivity, component emergence, and degree distributions in real-world networks.

Contribution

The paper presents the MAG model, a novel approach that links node attributes with network topology, and offers mathematical analysis of its properties.

Findings

MAG can produce networks with log-normal or power-law degree distributions.

Derived thresholds for connectivity and giant component emergence.

Networks modeled by MAG have a constant diameter.

Abstract

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.