Related papers: Non-equilibrium random walks on multiplex networks
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 diffusion on a multilayer network where the contact dynamics between the nodes is governed by a random process and where the waiting time distribution differs for edges from different layers. We study the impact on a random walk of…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm, however, related theoretical results are much less…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social…
We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of…
This paper considers a class of non-Markovian discrete-time random processes on a finite state space {1,...,d}. The transition probabilities at each time are influenced by the number of times each state has been visited and by a fixed a…
We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks…
Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be…
Elements composing complex systems usually interact in several different ways and as such the interaction architecture is well modelled by a multiplex network. However often this architecture is hidden, as one usually only has experimental…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
The mean first passage time~(MFPT) of random walks is a key quantity characterizing dynamic processes on disordered media. In a random fractal embedded in the Euclidean space, the MFPT is known to obey the power law scaling with the…
A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
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…
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global…
We study the statistics of the first passage of a random walker to absorbing subsets of the boundary of compact domains in different spatial dimensions. We describe a novel diagnostic method to quantify the trajectory-to-trajectory…