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Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…

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.…

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…

Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey…

I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often…

We are interested in modeling networks in which the connectivity among the nodes and node attributes are random variables and interact with each other. We propose a probabilistic model that allows one to formulate jointly a probability…

Recent advances in computational methods for intractable models have made network data increasingly amenable to statistical analysis. Exponential random graph models (ERGMs) emerged as one of the main families of models capable of capturing…

We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We provide the first general results on when these…

The structure of large-scale social networks has predominantly been articulated using generative models, a form of average-case analysis. This chapter surveys recent proposals of more robust models of such networks. These models posit…

The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via…

We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…

Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…

We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…

Researchers interested in statistically modeling network data have a well-established and quickly growing set of approaches from which to choose. Several of these methods have been regularly applied in research on political networks, while…

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

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…

We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…