Related papers: Efficient network exploration by means of resettin…
We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are…
In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the…
We investigate network exploration by random walks defined via stationary and adaptive transition probabilities on large graphs. We derive an exact formula valid for arbitrary graphs and arbitrary walks with stationary transition…
We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability $r$. We construct a discrete renewal…
Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
Network science has emerged as a powerful tool through which we can study the higher-order architectural properties of the world around us. How human learners exploit this information remains an essential question. Here, we focus on the…
Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…
The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms of three parameters which control the probability of,…
Biomolecular networks, such as protein-protein interactions, gene-gene associations, and cell-cell interactions, offer valuable insights into the complex organization of biological systems. These networks are key to understanding cellular…
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
Our objective is to sample the node set of a large unknown graph via crawling, to accurately estimate a given metric of interest. We design a random walk on an appropriately defined weighted graph that achieves high efficiency by…
This work addresses the superdiffusive motion of a discrete time random walker on ordered discrete substrates and complex networks with the presence of long-range interactions (LRIs). In ordered regular lattices, where LRIs have a clear…
This work is motivated by the study of some two-dimensional random walks in random environment (RWRE) with transition probabilities independent of one coordinate of the walk. These are non-reversible models and can not be treated by…
Reinforced random walks (RRWs), including vertex-reinforced random walks (VRRWs) and edge-reinforced random walks (ERRWs), model random walks where the transition probabilities evolve based on prior visitation history~\cite{mgr, fmk,…