Related papers: Random Graph Models and Matchings

Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…

This is a companion piece to my paper on "Example-Based Procedural Modeling Using Graph Grammars." This paper examines some of the theoretical issues in more detail. This paper discusses some more complex parts of the implementation, why…

This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…

First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…

This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…

Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\"os-R\'enyi random graphs, where edges are independent.…

We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011)…

Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…

Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability…

Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…

Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…

Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features,…

We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…

The goal of this paper is to describe the connections between Perron-Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron-Frobenius theory gives results about the sets of integers that can arise as periods of…

Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…

We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…