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An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…

Social networks are rarely observed in full detail. In many situations properties are known for only a sample of the individuals in the network and it is desirable to induce global properties of the full social network from this…

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this…

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.…

Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

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…

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…

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…

Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…

We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in an underlying similarity space and uses rewirings of the…

Network science has been extensively developed to characterize structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally…

We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of…

When re-structuring patient cohorts into so-called population graphs, initially independent data points can be incorporated into one interconnected graph structure. This population graph can then be used for medical downstream tasks using…

Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…

Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade the overabundance of certain sub-network patterns, so called motifs, has attracted…

Bayesian inference for exponential family random graph models (ERGMs) is a doubly-intractable problem because of the intractability of both the likelihood and posterior normalizing factor. Auxiliary variable based Markov Chain Monte Carlo…

We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation…

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…