相关论文: Random Graph Models with Hidden Color

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…

Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…

Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…

Given a graphical degree sequence ${\bf d}=(d_1,\ldots, d_n)$, let $G(n, {\bf d})$ denote a uniformly random graph on vertex set $[n]$ where vertex $ i$ has degree $d_i$ for every $1\le i\le n$. We give upper and lower bounds on the joint…

In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…

A graph $H$ is said to be common if the number of monochromatic labelled copies of $H$ in a red/blue edge colouring of a large complete graph is asymptotically minimized by a random colouring with an equal proportion of each colour. We…

We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…

We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…

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…

The theory of colorful graphs can be developed by working in Galois field modulo (p), p > 2 and a prime number. The paper proposes a program of possible conversion of graph theory into a pleasant colorful appearance. We propose to paint the…

In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…

The Rado Graph, sometimes also known as the (countable) Random Graph, can be generated almost surely by putting an edge between any pair of vertices with some fixed probability $p \in (0, 1)$, independently of other pairs. In this article,…

In the first part of this paper, we consider weighted domination in the case where the vertices of the complete graph on~\(n\) vertices are equipped with independent and identically distributed (i.i.d.) weights. We use the probabilistic…

We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables which control the appearance of links between node pairs. We derive analytic expressions for the degree…

Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…

It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…

In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…

In this paper, we study orthogonal colourings of random geometric graphs. Two colourings of a graph are orthogonal if they have the property that when two vertices receive the same colour in one colouring, then those vertices receive…