Related papers: An approximation for return time distributions of …
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…
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 propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…
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…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer…
The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\tau\ll N$, the computed mean first passage time (MFPT), which…
The purpose of this short note is to establish a connection between a one-dimensional random walk in a random sparse environment and the random pinning model. We show that the grand canonical partition function of the pinning model…
In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative $(1+\delta)$ of uniform in expected…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting…
We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This…