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The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…

This paper reviews, classifies and compares recent models for social networks that have mainly been published within the physics-oriented complex networks literature. The models fall into two categories: those in which the addition of new…

Homophily, the tendency of individuals who are alike to form ties with one another, is an important concept in the study of social networks. Yet accounting for homophily effects is complicated in the context of bipartite networks where ties…

Motivated by the increasing abundance of data describing real-world networks that exhibit dynamical features, we propose an extension of the Exponential Random Graph Models (ERGMs) that accommodates the time variation of its parameters.…

Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant…

Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be modelled as stochastic processes, expanding…

In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…

Full probability models are critical for the statistical modeling of complex networks, and yet there are few general, flexible and widely applicable generative methods. We propose a new family of probability models motivated by the idea of…

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection based approaches (e.g. the…

Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…

The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging…

Large language models (LLMs) have become a popular approach for simulating human behaviors, yet it remains unclear if LLMs are necessary for all simulation tasks. We study a broad family of close-ended simulation tasks, with applications…

Graph embedding has been widely applied in areas such as network analysis, social network mining, recommendation systems, and bioinformatics. However, current graph construction methods often require the prior definition of neighborhood…

Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for…

Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…

In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…

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…

Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…

In this paper we describe the main featuress of the Bergm package for the open-source R software which provides a comprehensive framework for Bayesian analysis for exponential random graph models: tools for parameter estimation, model…

Human decision making underlies data generating process in multiple application areas, and models explaining and predicting choices made by individuals are in high demand. Discrete choice models are widely studied in economics and…