相关论文: Random Walks and Electric Networks

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…

This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…

Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting…

Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…

Random walks on a group $G$ model many natural phenomena. A random walk is defined by a probability measure $p$ on $G$. We are interested in asymptotic properties of the random walks and in particular in the linear drift and the asymptotic…

Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the numerical evaluation of various characteristics of such processes has received relatively little attention. This paper develops…

We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random…

Network science has become a powerful tool to describe the structure and dynamics of real-world complex physical, biological, social, and technological systems. Largely built on empirical observations to tackle heterogeneous, temporal, and…

Since the 1980s, and particularly with the Hopfield model, recurrent neural networks or RNN became a topic of great interest. The first works of neural networks consisted of simple systems of a few neurons that were commonly simulated…

We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin…

Associated to a random walk on $\mathbb{Z}$ and a positive integer $n$, there is a return probability of the random walk returning to the origin after $n$ steps. An interesting question is when the set of return probabilities uniquely…

In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…

In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…

A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…

Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics.…

We propose a link prediction algorithm that is based on spring-electrical models. The idea to study these models came from the fact that spring-electrical models have been successfully used for networks visualization. A good network…

Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…

The analytic properties of the Markov operator associated to a random walk are common tools in the study of the behaviour and some probabilistic features related to the walk. In this paper we consider a class of Markov operators which…