Related papers: Random Walks and Electric Networks
This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…
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…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
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…
Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…
A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
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…
Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected networks…
The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…
A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…
A complex web of roads, walkways and public transport systems can hide areas of geographical isolation very difficult to analyze. Random walks are used to spot the structural details of urban fabric.
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic…
This is a report of a scientific project carried out at Ecole Centrale Casablanca in 2019. This work is an entry into the world of Random Walk in a Random Environment (RWRE). We will discuss some intuitive concepts such as recurrence,…
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…