Related papers: An explicit formula of hitting times for random wa…
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…
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.
In this paper, we provide an exact formula for the average hitting times in a wheel graph $W_{N+1}$ using a combinatorial approach. For this wheel graph, the average hitting times can be expressed using Fibonacci numbers when the number of…
We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…
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…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
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 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…
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…
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…
We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…
We investigate the average hitting times of simple random walks on the $k$-th power graph $C_N^k$ of the cycle graph $C_N$. First, we show that the average hitting times are characterized by a difference equation corresponding to the graph…
Graph products have been extensively applied to model complex networks with striking properties observed in real-world complex systems. In this paper, we study the hitting times for random walks on a class of graphs generated iteratively by…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
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,…
We exhibit a close connection between hitting times of the simple random walk on a graph, the Wiener index, and related graph invariants. In the case of trees we obtain a simple identity relating hitting times to the Wiener index. It is…
Random walk based distributed algorithms make use of a token that circulates in the system according to a random walk scheme to achieve their goal. To study their efficiency and compare it to one of the deterministic solutions, one is led…
A survey is presented of known results concerning simple random walk on the class of distance-regular graphs. One of the highlights is that electric resistance and hitting times between points can be explicitly calculated and given strong…
We study nonconcentration of hitting times for simple random walk on finite graphs. We prove that, for every connected graph with $n$ vertices, \[ \operatorname{Var}_x(\tau_y)+\mathbb E_x\tau_y \ge \frac{(\mathbb E_x\tau_y)^2}{1+\log n}, \]…
Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…