Related papers: The interpolation method for random graphs with pr…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
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…
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 classify modules and rings with some specific properties of their intersection graphs. In particular, we describe rings with infinite intersection graphs containing maximal left ideals of finite degree. This answers a question raised in…
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. This confirms a conjecture made in 1997. As a result, many interesting functions of…
We establish the existence of free energy limits for several combinatorial models on Erd\"{o}s-R\'{e}nyi graph $\mathbb {G}(N,\lfloor cN\rfloor)$ and random $r$-regular graph $\mathbb {G}(N,r)$. For a variety of models, including…
This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the…
Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and…
We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…
We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…
In this paper we consider the optimization problem of generating graphs with a prescribed degree distribution, such that the correlation between the degrees of connected nodes, as measured by Spearman's rho, is minimal. We provide an…
In this paper, we present two localized graph filtering based methods for interpolating graph signals defined on the vertices of arbitrary graphs from only a partial set of samples. The first method is an extension of previous work on…
We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…
We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…