Related papers: Distinct scalings for mean first-passage time of r…
Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
We consider a random walk in confined geometry, starting from a site and eventually reaching a target site. We calculate analytically the distribution of the occupation time on a third site, before reaching the target site. The obtained…
We extend the standard scale-free network model to include a ``triad formation step''. We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model…
We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the particle jumping rate function $p(n)=n^\delta$. We show analytically…
We investigate scaling properties of human brain functional networks in the resting-state. Analyzing network degree distributions, we statistically test whether their tails scale as power-law or not. Initial studies, based on least-squares…
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…
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},…
Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks…
What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…
We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…
We investigate a self-interacting random walk, whose dynamically evolving environment is a random tree built by the walker itself, as it walks around. At time $n=1,2,\dots$, right before stepping, the walker adds a random number (possibly…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
We study discrete random walks on the NFSFT and provide new methods to calculate the analytic solutions of the MFPT for any pair of nodes, the MTT for any target node and MDT for any source node. Further more, using the MTT and the MDT as…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
In this article, we investigate an artificial traffic model on scale-free networks. Instead of using the routing strategy of the shortest path, a generalized routing algorithm is introduced to improve the transportation throughput, which is…
Recent works have explored the properties of L\'evy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT)…
We present analytical results for the distribution of first hitting times of non-backtracking random walks on finite Erd\H{o}s-R\'enyi networks of $N$ nodes. The walkers hop randomly between adjacent nodes on the network, without stepping…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…