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This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…
In recent years, the Graph Model has become increasingly popular, especially in the application domain of social networks. The model has been semantically augmented with properties and labels attached to the graph elements. It is difficult…
Recently much attention has been paid to deep generative models, since they have been used to great success for variational inference, generation of complex data types, and more. In most all of these settings, the goal has been to find a…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…
Social networks exhibit strikingly systematic patterns across a wide range of human contexts. While genetic variation accounts for a significant portion of the variation in many complex social behaviors, the heritability of egocentric…
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
Temporal networks are suitable for modeling complex evolving systems. It has a wide range of applications, such as social network analysis, recommender systems, and epidemiology. Recently, modeling such dynamic systems has drawn great…
We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to…
Graph neural networks (GNNs) have demonstrated success in modeling relational data, especially for data that exhibits homophily: when a connection between nodes tends to imply that they belong to the same class. However, while this…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
Nodes in real-world networks are usually organized in local modules. These groups, called communities, are intuitively defined as sub-graphs with a larger density of internal connections than of external links. In this work, we introduce a…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured…
The emergence of social networks and the definition of suitable generative models for synthetic yet realistic social graphs are widely studied problems in the literature. By not being tied to any real data, random graph models cannot…
We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as…