Related papers: Stationary distribution of node2vec random walks o…

In this paper, we propose QWalkVec, a quantum walk-based node embedding method. A quantum walk is a quantum version of a random walk that demonstrates a faster propagation than a random walk on a graph. We focus on the fact that the effect…

We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…

We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…

In this paper we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition probabilities dictate the flow of random walkers through the network, nonlinear…

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…

Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…

We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…

We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…

The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…

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…

A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often (with ties broken randomly). The properties of self-repelling random walks have been analyzed…

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 study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…

We discuss various models for epidemics on networks that rely on Markov chains. Random walks on graphs are often used to predict epidemic spread and to investigate possible control actions to mitigate them. In this study, we demonstrate…

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 embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on…

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from…

Over the last few years, network science has proved to be useful in modeling a variety of complex systems, composed of a large number of interconnected units. The intricate pattern of interactions often allows the system to achieve complex…

RDF2vec is a technique for creating vector space embeddings from an RDF knowledge graph, i.e., representing each entity in the graph as a vector. It first creates sequences of nodes by performing random walks on the graph. In a second step,…

Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility.…