Related papers: Characterizing network topology using first-passag…
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…
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…
We present a general framework, applicable to a broad class of random walks on complex networks, which provides a rigorous lower bound for the mean first-passage time of a random walker to a target site averaged over its starting position,…
In this work we consider a class of recursively-grown fractal networks $G_n(t)$, whose topology is controlled by two integer parameters $t$ and $n$. We first analyse the structural properties of $G_n(t)$ (including fractal dimension,…
Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
Consider a network embedded in the 2D plane, where a particle diffuses along the edges of the network. It is clear that over short length scales a particle moves along a single edge and thus undergoes one-dimensional diffusion. However, on…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade1. The importance of FPTs originates from…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
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…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
The possibility to identify the nature (e.g. random or scale free) of complex networks while performing respective random walks is investigated with respect to autonomous agents based on Bayesian decision theory and humans navigating…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
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 derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
The transport properties of discrete-time random walks on ring networks with deterministic shortcuts are investigated through analytical and numerical methods. The network consists of a periodic chain where each node is connected to its…
We introduce a formalism based on a continuous time approximation, to study the characteristics of Page Rank random walks. We find that the diffusion of the occupancy probability has a dynamics that exponentially "forgets" the initial…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using "traceroute"-like probes. This methodology, akin to the merging of different spanning trees to a set of destinations, has been argued to…