Related papers: Graph sequences sampled from Robinson graphons

Let $\Gamma$ denote a distance-regular graph with diameter $D\geq 3$. Juri\v{s}i\'c and Vidali conjectured that if $\Gamma$ is tight with classical parameters $(D,b,\alpha,\beta)$, $b\geq 2$, then $\Gamma$ is not locally the block graph of…

Graph neural networks (GNNs) have been widely used in graph-related contexts. It is known that the separation power of GNNs is equivalent to that of the Weisfeiler-Lehman (WL) test; hence, GNNs are imperfect at identifying all…

A Robinson similarity matrix is a symmetric matrix where the entry values on all rows and columns increase toward the diagonal. Decompose the Robinson matrix into the sum of k {0, 1}-matrices, then these k {0, 1}-matrices are the adjacency…

The local tree-width of a graph G=(V,E) is the function ltw^G: N -> N that associates with every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with…

We study graphons as a non-parametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. Our algorithms and analysis go beyond previous work in several…

We examined the properties of the coefficients of the \cite{lanczos1964} approximation of the $\Gamma$-function with complex values of the free parameter together with the convergence properties of the approximation when using these…

We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A…

Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying stochastic process of a signal that can take on a bounded…

In this paper, we present a very accurate approximation for gamma function: \begin{equation*} \Gamma \left( x+1\right) \thicksim \sqrt{2\pi x}\left( \dfrac{x}{e}\right) ^{x}\left( x\sinh \frac{1}{x}\right) ^{x/2}\exp \left(…

Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…

We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based…

In two recent papers by Veitch and Roy and by Borgs, Chayes, Cohn, and Holden, a new class of sparse random graph processes based on the concept of graphexes over $\sigma$-finite measure spaces has been introduced. In this paper, we…

Consider a non-elementary Gromov-hyperbolic group $\Gamma$ with a suitable invariant hyperbolic metric, and an ergodic probability measure preserving (p.m.p.) action on $(X,\mu)$. We construct special increasing sequences of finite subsets…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

Given a bounded open set $\Omega\subset \mathbb{R}^n$, we study sequences of quadratic functionals on the Sobolev space $H^1_0(\Omega)$, perturbed by sequences of bounded linear functionals. We prove that their $\Gamma$-limits, in the weak…

We construct a family of countexamples to a conjecture of Galvin [5], which stated that for any $n$-vertex, $d$-regular graph $G$ and any graph $H$ (possibly with loops), \[\hom(G,H) \leq \max\left\lbrace\hom(K_{d,d}, H)^{\frac{n}{2d}},…

Graph convolutional networks (GCNs) are powerful deep neural networks for graph-structured data. However, GCN computes the representation of a node recursively from its neighbors, making the receptive field size grow exponentially with the…

Local convergence techniques have become a key methodology to study sparse random graphs. However, convergence of many random graph properties does not directly follow from local convergence. A notable, and important, such random graph…

Let $\Gamma_{k}(V)$ be the Grassmann graph formed by $k$-dimensional subspaces of an $n$-dimensional vector space over the finite field ${\mathbb F}_{q}$ consisting of $q$ elements and $1<k<n-1$. Denote by $\Gamma(n,k)_q$ the restriction of…

The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…