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Network data are increasingly available in various research fields, motivating statistical analysis for populations of networks where a network as a whole is viewed as a data point. Due to the non-Euclidean nature of networks, basic…

We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased…

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the…

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…

We develop a new class of random graph models for the statistical estimation of network formation -- subgraph generated models (SUGMs). Various subgraphs -- e.g., links, triangles, cliques, stars -- are generated and their union results in…

This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…

Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of…

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…

Exponential-family random graph models (ERGMs) are probabilistic network models that are parametrized by sufficient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing system…

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in…

Data in the form of graphs, or networks, arise naturally in a number of contexts; examples include social networks and biological networks. We are often faced with the availability of multiple graphs on a single set of nodes. In this…

We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…

This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…