Related papers: Expected hitting time estimates on finite graphs
The hitting time, h_uv, of a random walk on a finite graph G, is the expected time for the walk to reach vertex v given that it started at vertex u. We present two methods of calculating the hitting time between vertices of finite graphs,…
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…
In the present paper, we give the exact formula for the average hitting time (HT, as an abbreviation) of random walks from one vertex to any other vertex on the some weighted Cayley graphs.
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
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…
We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the variance of hitting times. For a simple random walk on a…
For random walks on graph $\mathcal{G}$ with $n$ vertices and $m$ edges, the mean hitting time $H_j$ from a vertex chosen from the stationary distribution to vertex $j$ measures the importance for $j$, while the Kemeny constant…
Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…
It is known that the average hitting times of simple random walks from any vertex to any other vertex in distance-regular graphs are determined by their intersection array. In this paper, we introduce a new graph classification called…
We consider simple random walk on a realization of an Erd\H{o}s-R\'enyi graph that is asymptotically almost surely (a.a.s.) connected. We show a Central Limit Theorem (CLT) for the average starting hitting time, i.e. the expected time it…
Consider a simple random walk on a realization of an Erd\H{o}s-R\'enyi graph. Assume that it is asymptotically almost surely (a.a.s.) connected. Conditional on an eigenvector delocalization conjecture, we prove a Central Limit Theorem (CLT)…
Next to the shortest path distance, the second most popular distance function between vertices in a graph is the commute distance (resistance distance). For two vertices u and v, the hitting time H_{uv} is the expected time it takes a…
In this work we consider a simple random walk embedded in a generic branched structure and we find a close-form formula to calculate the hitting time $H\left(i,f\right)$ between two arbitrary nodes $i$ and $j$. We then use this formula to…
Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However,…
The exact formula for the average hitting time (HT, as an abbreviation) of simple random walks from one vertex to any other vertex on the square $C^2_N$ of an $N$-vertex cycle graph $C_N$ was given by N. Chair [\textit{Journal of…
We consider Erd\H{o}s-R\'enyi graphs $G(n,p)$ for $0 < p < 1$ fixed and $n \rightarrow \infty$ and study the expected number of steps, $H_{wv}$, that a random walk started in $w$ needs to first arrive in $v$. A natural guess is that an…
In this paper, following the paper ``On the average hitting times of the squares of cycles,'' we provide an explicit formula for the average hitting times of a simple random walk on a directed graph with $N$ vertices, where the graph…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{\rm hit}$, both in terms of the relaxation time. We also prove a…
A close relation between hitting times of the simple random walk on a graph, the Kirchhoff index, resistance-centrality, and related invariants of unicyclic graphs is displayed. Combining with the graph transformations and some other…