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In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and…
We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…
In this paper we investigate the spectral and the scattering theory of Gauss--Bonnet operators acting on perturbed periodic combinatorial graphs. Two types of perturbation are considered: either a multiplication operator by a short-range or…
Given a graph $G$, the hard-core model defines a probability distribution over its independent sets, assigning to each set of size $k$ a probability of $\frac{\lambda^k}{Z}$, where $\lambda>0$ is a parameter known as the \emph{fugacity} and…
The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. For certain monoids connected with combinatorics, such as the plactic monoid (the monoid…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Bipartite graph tiling was studied by Zhao who gave the best possible minimum degree conditions for a balanced bipartite graph on 2ms vertices to contain m vertex disjoint copies of K_{s,s}. Let s<t be fixed positive integers. Hladk\'y and…
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…
In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density. Our results imply several new bounds for classical problems in graph Ramsey theory and improve…
Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.
Discrete-time switched linear systems where switchings are governed by a digraph are considered. The minimum (or average) dwell time that guarantees the asymptotic stability can be computed by calculating the maximum cycle ratio (or maximum…
Given the adjacency matrix of an undirected graph, we define a coupling of the spectral measures at the vertices, whose moments count the rooted closed paths in the graph. The resulting joint spectral measure verifies numerous interesting…
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from a theoretical framework that we developed based on…
Let $G$ be a graph. The {\em spectral radius} of $G$ is the largest eigenvalue of its adjacency matrix. For a non-complete bipartite graph $G$ with parts $X$ and $Y$, the {\em bipartite toughness} of $G$ is defined as…
Let $G$ be a group and $L(G)$ be the set of all subgroups of $G$. We introduce a bipartite graph $\mathcal{B}(G)$ on $G$ whose vertex set is the union of two sets $G \times G$ and $L(G)$, and two vertices $(a, b) \in G \times G$ and $H \in…
Unmixed bipartite graphs have been characterized by Ravadra and Villarreal independently. Our aim in this paper is to characterize unmixed r-partite graphs under a certain condition, witch is a generalization of villarreal's theorem on…
A connected dominating set (CDS) in a graph is a dominating set of vertices that induces a connected subgraph. Having many disjoint CDSs in a graph can be considered as a measure of its connectivity, and has various graph-theoretic and…
The maximum matching width is a width-parameter that is defined on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the…
An $(m,n)$-mixed graph generalizes the notions of oriented graphs and edge-coloured graphs to a graph object with $m$ arc types and $n$ edge types. A simple colouring of such a graph is a non-trivial homomorphism to a reflexive target. We…
This paper investigates the relationship between graph convolution and Mixup techniques. Graph convolution in a graph neural network involves aggregating features from neighboring samples to learn representative features for a specific node…