Related papers: Stationary distribution of node2vec random walks o…

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…

Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…

Recent years have witnessed a surge of interest in machine learning on graphs and networks with applications ranging from vehicular network design to IoT traffic management to social network recommendations. Supervised machine learning…

In the voter model, vertices of a graph (interpreted as voters) adopt one out of two opinions (0 and 1), and update their opinions at random times by copying the opinion of a neighbor chosen uniformly at random. This process is dual to a…

In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…

Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn…

In this article we study the distribution of the number of points of a simple random walk, visited a given number of times (the k-multiple point range). In a previous article we had developed a graph theoretical approach which is now…

We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…

We develop a framework for designing density-dependent stochastic resetting protocols to regulate distributions of random walkers on networks. Resetting mechanisms that depend on local densities induce correlations in otherwise…

The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling…

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…

We investigate by random-walk simulations and a mean-field theory how growth by biased addition of nodes affects flow of the current through the emergent conducting graph, representing a digital circuit. In the interior of a large network…

Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…

In this note, we compute the probability that a two-dimensional symmetric random walk visits more vertices than expected, for deviations on scales between the mean behavior and linear growth.

The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…

We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

The potential for machine learning systems to amplify social inequities and unfairness is receiving increasing popular and academic attention. Much recent work has focused on developing algorithmic tools to assess and mitigate such…

This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…

RDF2vec is a knowledge graph embedding mechanism which first extracts sequences from knowledge graphs by performing random walks, then feeds those into the word embedding algorithm word2vec for computing vector representations for entities.…