Related papers: The Laplacian Spectrum of Large Graphs Sampled fro…
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…
Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…
I prove that the spectrum of the Laplace-Beltrami operator with the Neumann boundary condition on a compact Riemannian manifold with boundary admits a fast approximation by the spectra of suitable graph Laplacians on proximity graphs on the…
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…
We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are…
We prove that the Dirichlet eigenvalues of the Laplace-Beltrami operator on a compact Riemannian manifold with cylindrical boundary can be approximated by the spectrum of truncated graph Laplacians constructed from…
Let $G$ be a simple graph with $n$ vertices and let $$C(G;x)=\sum_{k=0}^n(-1)^{n-k}c(G,k)x^k$$ denote the Laplacian characteristic polynomial of $G$. Then if the size $|E(G)|$ is large compared to the maximum degree $\Delta(G)$, Laplacian…
In this note, we show how to obtain a "characteristic power series" of graphons -- infinite limits of dense graphs -- as the limit of normalized reciprocal characteristic polynomials. This leads to a new characterization of graph…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solve the problem for Cartesian powers of arbitrary graphs. In detail, let $G$ be a connected graph on $k$…
In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result…
We consider a dynamic Erd\H{o}s-R\'enyi random graph (ERRG) on $n$ vertices in which each edge switches on at rate $\lambda$ and switches off at rate $\mu$, independently of other edges. The focus is on the analysis of the evolution of the…
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…
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
Following our work on the graph of the Weierstrass function, in the spirit of those of J. Kigami and R. S. Strichartz, which enabled us to build a Laplacian on the aforementioned graph, it was natural to go further and give the related…
In this paper, we present two new matrices, namely the resistance Laplacian and resistance signless Laplacian matrix of a connected graph. We provide a generalized form of these matrices for different classes of graphs, including the…
We show a norm convergence result for the Laplacian on a class of post-critically finite fractals with arbitrary Borel regular probability measure which can be approximated by a sequence of finite-dimensional graph Laplacians with…