Related papers: Estimating Random-Walk Probabilities in Directed G…
Graphs are useful structures that can model several important real-world problems. Recently, learning graphs have drawn considerable attention, leading to the proposal of new methods for learning these data structures. One of these studies…
Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…
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 investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
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…
Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…
In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Although it has the same computational complexity and shares…
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…
We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of $t$-periodic walks and its mean, when the cardinality of the…
The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We introduce a new notion…
PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the…
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
We present analytical results for the joint probability distribution $P(T_{FR}=t,S=s)$ of first return (FR) times t and of the number of distinct sites s visited by a random walk (RW) on a one dimensional lattice before returning to the…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
We present analytical results for the distribution of first hitting times of random walks (RWs) on random regular graphs (RRGs) of degree $c \ge 3$ and a finite size $N$. Starting from a random initial node at time $t=1$, at each time step…
We study the biased random walk where at each step of a random walk a "controller" can, with a certain small probability, move the walk to an arbitrary neighbour. This model was introduced by Azar et al. [STOC'1992]; we extend their work to…
We study a continuous time branching process where an individual splits into two daughters with rate b and dies with rate a, starting from a single individual at t=0. We show that the model can be mapped exactly to a random walk problem…
We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth is random and its length equals lambda^{N-1}, with lambda<1. As lambda increases past a critical value lambda_c, the endpoint…