Related papers: Embedding networks with the random walk first retu…

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…

We derive a general formula for computing the expected first return time of a random walk on a finite graph. Using this framework, we calculate the expected first return time in various settings over bounded rectangular grids with different…

Random walk-based node embedding algorithms have attracted a lot of attention due to their scalability and ease of implementation. Previous research has focused on different walk strategies, optimization objectives, and embedding learning…

Node embedding aims to map nodes in the complex graph into low-dimensional representations. The real-world large-scale graphs and difficulties of labeling motivate wide studies of unsupervised node embedding problems. Nevertheless, previous…

Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…

Network representation learning (NRL) methods aim to map each vertex into a low dimensional space by preserving the local and global structure of a given network, and in recent years they have received a significant attention thanks to…

Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…

Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…

In the field of node representation learning the task of interpreting latent dimensions has become a prominent, well-studied research topic. The contribution of this work focuses on appraising the interpretability of another…

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 are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…

We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an…

In this paper, we propose a general framework for the trapping problem on a weighted network with a perfect trap fixed at an arbitrary node. By utilizing the spectral graph theory, we provide an exact formula for mean first-passage time…

We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits…

Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer…

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 propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous…

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…

Analytical results for the distribution of first hitting times of random walks on Erd\H{o}s-R\'enyi networks are presented. Starting from a random initial node, a random walker hops between adjacent nodes until it hits a node which it has…

We perform an in-depth study for mean first-passage time (MFPT)---a primary quantity for random walks with numerous applications---of maximal-entropy random walks (MERW) performed in complex networks. For MERW in a general network, we…