Related papers: Random walks with resetting on hypergraph

In relation extraction, a key process is to obtain good detectors that find relevant sentences describing the target relation. To minimize the necessity of labeled data for refining detectors, previous work successfully made use of…

We revisit an old minor topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and…

We study random walks on the giant component of Hyperbolic Random Graphs (HRGs), in the regime when the degree distribution obeys a power law with exponent in the range $(2,3)$. In particular, we first focus on the expected time for a…

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,…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

Graph embedding maps a graph into a convenient vector-space representation for graph analysis and machine learning applications. Many graph embedding methods hinge on a sampling of context nodes based on random walks. However, random walks…

We investigate the first passage time beyond a barrier located at $b\geq0$ of a random walk with independent and identically distributed jumps, starting from $x_0=0$. The walk is subject to stochastic resetting, meaning that after each step…

Message-passing graph neural networks (GNNs) excel at capturing local relationships but struggle with long-range dependencies in graphs. In contrast, graph transformers (GTs) enable global information exchange but often oversimplify the…

Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this…

It is known that the stationary distribution of the random walk process is dependent on the structure of the network. This could provide us a solution of the network reconstruction. However, the stationary distribution of the random walk…

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…

The betweenness centrality of graphs using random walk paths instead of geodesics is studied. A scaling collapse with no adjustable parameters is obtained as the graph size $N$ is varied; the scaling curve depends on the graph model. A…

We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…

We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…

Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph…

We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…

Network representation learning has aroused widespread interests in recent years. While most of the existing methods deal with edges as pairwise relationships, only a few studies have been proposed for hyper-networks to capture more…

We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…

Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to…

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…