Related papers: Random Graph Models and Matchings
Graph matching is an important problem in machine learning and pattern recognition. Herein, we present theoretical and practical results on the consistency of graph matching for estimating a latent alignment function between the vertex sets…
We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…
In this paper, matching pairs of stocahstically generated graphs in the presence of generalized seed side-information is considered. The graph matching problem emerges naturally in various applications such as social network…
Graph Retrieval has witnessed continued interest and progress in the past few years. In thisreport, we focus on neural network based approaches for Graph matching and retrieving similargraphs from a corpus of graphs. We explore methods…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…
We consider two independent Erd\H{o}s-R\'enyi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters…
In this note, we investigate fundamental relations between exploration processes in random graphs, and branching processes. We formulate a class of models that we call {\em rank-$k$ random graphs}, and that are special in that their…
We consider the number of crossings in a graph which is embedded randomly on a convex set of points. We give an estimate to the normal distribution in Kolmogorov distance which implies a convergence rate of order $n^{-1/2}$ for various…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
The problem of aligning Erd\"os-R\'enyi random graphs is a noisy, average-case version of the graph isomorphism problem, in which a pair of correlated random graphs is observed through a random permutation of their vertices. We study a…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
We present a novel approach for finding multiple noisily embedded template graphs in a very large background graph. Our method builds upon the graph-matching-matched-filter technique proposed in Sussman et al., with the discovery of…