Multiplicative Attribute Graph Model of Real-World Networks

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.

Sampling of Attributed Networks from Hierarchical Generative Models

“…There is work in this direction. One example is the multiplicative attribute graph (MAG) model [10]. However, the evaluation of AGM [16] showed that MAG underperformed AGM for sampling new networks because MAG considers latent node attributes instead of learning from observed node attributes.…”

“…With Ne and β, it determines Γ (the total number of edges per type that must be sampled to match ρIN ). Edge sampling is realized by the FOR loop (lines [8][9][10][11][12][13][14]. This loop calculates the number of edges per edge-type Y to be sampled given a unique probability πu (line 9).…”

“…The ability to generate network structure has served to support research in the basic area of network science but to date there are few methods to generate networks with correlated node attributes [10] [16]. Furthermore, few can replicate the range of complex characteristics that occur in real world networks.…”

Homophily in networked agent-based models: a method to generate homophilic attribute distributions to improve upon random distribution approaches

“…A common way to include the homophily effect in ABMs is to utilize a network generator that uses a higher chance to generate links between similar individuals [6,16,19,24]. However, since the proportions of population shares have a direct effect on link formation and thus topology, the resulting network may differ from a network that is generated by an unbiased generator.…”

Classification and prediction of matrix structured data with applications to recommendation systems, identifying anti-socials and bot-nets

“…Inspired by PCA and SVD, in Cliqster we choose to represent Z in a new space [27], [40]. Community structure is a key factor to understand and analyze a network, and because of this we are motivated to choose bases in a way that reflects the community structure [38].…”