Related papers: Random Walk Access Times on Partially-Disordered C…
The determination of mean first-passage time (MFPT) for random walks in networks is a theoretical challenge, and is a topic of considerable recent interest within the physics community. In this paper, according to the known connections…
Random walks by single-node agents have been systematically conducted on various types of complex networks in order to investigate how their topologies can affect the dynamics of the agents. However, by fitting any network node, these…
Extensive empirical investigation has shown that a plethora of real networks synchronously exhibit scale-free and modular structure, and it is thus of great importance to uncover the effects of these two striking properties on various…
Quantum walks on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder.…
We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
The diffusion process through an ideal polymer network is studied by applying the effective medium theory (EMT) to a lattice-gas model. Polymers are modeled by random walks on the lattice bonds, across which molecules can hop with a certain…
Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in determining not only the existence of cutoff and the order of…
We propose local-biased random walks on general networks where a Markovian walker can choose between different types of biases in each node to define transitions to its neighbors depending on their degrees. For this ergodic dynamics, we…
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…
The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short range memory. We derive the exact…
In this work, the outward and inward accessibilities of individual nodes are defined and their potential for application is illustrated with respect to the investigation of 6 different types of networks. The outward accessibility quantifies…
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 propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
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…
Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node…
We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…