Related papers: Random Walks on Simplicial Complexes and the norma…
Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different…
We introduce root-to-leaf path random walks on double covers of graded signed graphs and analyze their behavior in a general setting. Viewing simplicial complexes within this framework, we show that these walks induce the natural…
We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and analyze general random walk Laplacians for hypergraphs, and we…
In this paper, we introduce random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension $d$, a random walk with an absorbing state is defined which relates to the spectrum of the $k$-dimensional…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
In this paper, we analyze the eigenfunctions of the edge-based Laplacian on a graph and the relationship of these functions to random walks on the graph. We commence by discussing the set of eigenfunctions supported at the vertices, and…
Several variants of the graph Laplacian have been introduced to model non-local diffusion processes, which allow a random walker to {\textquotedblleft jump\textquotedblright} to non-neighborhood nodes, most notably the transformed path…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, $k$-dimensional "simplices") and how they are influenced through…
Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial…
Link partitioning is a popular approach in network science used for discovering overlapping communities by identifying clusters of strongly connected links. Current link partitioning methods are specifically designed for networks modelled…
Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
Random walks on a graph reflect many of its topological and spectral properties, such as connectedness, bipartiteness and spectral gap magnitude. In the first part of this paper we define a stochastic process on simplicial complexes of…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
Random walks on bounded degree expander graphs have numerous applications, both in theoretical and practical computational problems. A key property of these walks is that they converge rapidly to their stationary distribution. In this work…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…