Related papers: Walks on weighted networks
This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…
We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits…
We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength b_c exists such that most walks find the target within a finite time when b>b_c. For b<b_c,…
A Random Walk in Changing Environment (RWCE) is a weighted random walk on a locally finite, connected graph $G$ with random, time-dependent edge-weights. This includes self-interacting random walks, where the edge-weights depend on the…
We investigate the dynamics of simultaneous random walkers with resetting on networks and derive exact analytical expressions for the mean first-encounter times of Markovian random walkers. Specifically, we consider two cases for the…
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…
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 review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the…
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…
We analyze the Brownian Motion limit of a prototypical unit step reinforced random-walk on the half line. A reinforced random walk is one which changes the weight of any edge (or vertex) visited to increase the frequency of return visits.…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms of three parameters which control the probability of,…
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker-moves originates from the unitary interaction of the walker-coin with the qubit degrees of freedom in the quantum network. The…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
This paper presents an evolution model of weighted networks in which the structural growth and weight dynamics are driven by human behavior, i.e. passenger route choice behavior. Transportation networks grow due to people's increasing…
It has recently been shown that networks possessing scale-free and fractal properties may exhibit a bifractal nature, in which local structures are described by two different fractal dimensions. In this study, we investigate random walks on…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…