Related papers: Maximum entropy distributions on graphs
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based…
Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the $\beta$-model to weighted graphs. Similar to the $\beta$-model, each vertex in maximum entropy models is assigned a potential parameter,…
We study the problem of parameter estimation based on infection data from an epidemic outbreak on a graph. We assume that successive infections occur via contagion; i.e., transmissions can only spread across existing directed edges in the…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
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…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and…
Let $F_G(P)$ be a functional defined on the set of all the probability distributions on the vertex set of a graph $G$. We say that $G$ is \emph{symmetric with respect to $F_G(P)$} if the uniform distribution on $V(G)$ maximizes $F_G(P)$.…
We connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy coming from the vertex shift, which is related to the spectral radius of the graph's adjacency matrix, the…
The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
Chatterjee, Diaconis and Sly (2011) recently established the consistency of the maximum likelihood estimate in the $\beta$-model when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…
The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…