Related papers: Random walks on weighted networks
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
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 study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a…
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…
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 introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
Explicit determination of the mean first-passage time (MFPT) for trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e. node…
We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
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…
We consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
We perform an in-depth study for mean first-passage time (MFPT)---a primary quantity for random walks with numerous applications---of maximal-entropy random walks (MERW) performed in complex networks. For MERW in a general network, we…
We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks…
In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses…
A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…