Related papers: Maximum entropy distributions on graphs
A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
We consider classes of pseudo-random graphs on $n$ vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals $(np - Cn^\delta,np+Cn^\delta)$ and $(np^2- C n^\delta, np^2 +C…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list.…
We use a multivariate central limit theorem (CLT) to study the distribution of random geometric graphs (RGGs) on the cube and torus in the high-dimensional limit with general node distributions. We find that the distribution of RGGs on the…
Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…
We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We…
We exhibit the joint symmetric distribution of the following two parameters on the set of unlabeled, simple, connected graphs with $n$ vertices. The first parameter is the maximal number of leaves attached to a vertex. The second parameter…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We investigate the behavior of the empirical neighbourhood distribution of marked graphs in the framework of local weak convergence. We establish a large deviation principle for such families of empirical measures. The proof builds on…
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 develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least $(1-\eps)$…
Finding graph indices which are unbiased to network size and density is of high importance both within a given field and across fields for enhancing comparability of modern network science studies. The degree variance is an important metric…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…