Related papers: An Averaging Processes on Hypergraphs

Despite of the extreme success of the spectral graph theory, there are relatively few papers applying spectral analysis to hypergraphs. Chung first introduced Laplacians for regular hypergraphs and showed some useful applications. Other…

We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs). In this hypergraph model, the contribution of every vertex to each of its incident hyperedges is represented…

The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…

A total weighting of the vertices and edges of a hypergraph is called vertex-coloring if the total weights of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted…

For a fixed integer $r\geqslant 3$, let $\mathbb{H}_r(n,p)$ be a random $r$-uniform hypergraph on the vertex set $[n]$, where each $r$-set is an edge randomly and independently with probability $p$. The random $r$-generalized triadic…

Here we introduce connectivity operators, namely, diffusion operators, general Laplacian operators, and general adjacency operators for hypergraphs. These operators are generalisations of some conventional notions of apparently different…

In this paper, we give tight bounds for the normalized Laplacian eigenvalues of hypergraphs that are not necessarily uniform, and provide an edge version interlacing theorem, a Cheeger inequality, and a discrepancy inequality that are…

This paper proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It is proved that the…

A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this paper…

The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…

We study Aldous' conjecture that the spectral gap of the interchange process on a weighted undirected graph equals the spectral gap of the random walk on this graph. We present a conjecture in the form of an inequality, and prove that this…

In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the…

In this note we give a new upper bound for the Laplacian eigenvalues of an unweighted graph. Let $G$ be a simple graph on $n$ vertices. Let $d_{m}(G)$ and $\lambda_{m+1}(G)$ be the $m$-th smallest degree of $G$ and the $m+1$-th smallest…

We investigate first passage percolation on inhomogeneous random graphs. The random graph model G(n,kappa) we study is the model introduced by Bollob\'as, Janson and Riordan, where each vertex has a type from a type space S and edge…

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…

In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…

Networks and network processes have emerged as powerful tools for modeling social interactions, disease propagation, and a variety of additional dynamics driven by relational structures. Recently, neural networks have been generalized to…

This paper develops analityc methods for investigating uniform hypergraphs. Its starting point is the spectral theory of 2-graphs, in particular, the largest and the smallest eigenvalues of 2-graphs. On the one hand, this simple setup is…

For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the…

We consider the next greedy randomized process for generating maximal H-free graphs: Given a fixed graph H and an integer n, start by taking a uniformly random permutation of the edges of the complete n-vertex graph. Then, construct an…