Related papers: Random walks on complex networks with inhomogeneou…
Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are…
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…
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to…
Random walks are one of the best investigated dynamical processes on graphs. A particularly fascinating phenomenon is the scaling relationship of fluctuations $\sigma $ with the average flux $\langle f \rangle $. Here we analyze how network…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
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.…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and…
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…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
A power-law distance-dependent biased random walk model with a tuning parameter ($\sigma$) is introduced in which finite mean first passage times are realizable if $\sigma$ is less than a critical value $\sigma_c$. We perform numerical…
We study the random walk problem on a class of deterministic Scale-Free networks displaying a degree sequence for hubs scaling as a power law with an exponent $\gamma=\log 3/\log2$. We find exact results concerning different first-passage…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
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…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
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…
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…
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…