Related papers: Random Walk Models of Network Formation and Sequen…

Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…

Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: reconstructing all the past states of a network from…

Message-passing graph neural networks (GNNs) excel at capturing local relationships but struggle with long-range dependencies in graphs. In contrast, graph transformers (GTs) enable global information exchange but often oversimplify the…

Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…

In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected.…

We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…

Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans through graph partitioning. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest…

We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We…

In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…

Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…

Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…

Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled by the relative prevalence of a set of local sub-graph configurations…

In this article we focus on dynamic network data which describe interactions among a fixed population through time. We model this data using the latent space framework, in which the probability of a connection forming is expressed as a…

We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…

Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the…

In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…