Related papers: Random walks and community detection in hypergraph…

We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…

A hypergraph is a generalization of a graph that arises naturally when attribute-sharing among entities is considered. Compared to graphs, hypergraphs have the distinct advantage that they contain explicit communities and are more…

We propose a nonparametric approach to link prediction in large-scale dynamic networks. Our model uses graph-based features of pairs of nodes as well as those of their local neighborhoods to predict whether those nodes will be linked at…

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…

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,…

We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…

We study the problem of detecting a random walk on a graph from a sequence of noisy measurements at every node. There are two hypotheses: either every observation is just meaningless zero-mean Gaussian noise, or at each time step exactly…

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…

We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple…

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…

We introduce an analytical statistical method to characterize the communities detected in heterogeneous complex systems. By posing a suitable null hypothesis, our method makes use of the hypergeometric distribution to assess the probability…

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…

The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…

We propose a non-parametric link prediction algorithm for a sequence of graph snapshots over time. The model predicts links based on the features of its endpoints, as well as those of the local neighborhood around the endpoints. This allows…

Wildberger's construction enables us to obtain a hypergroup from a special graph via random walks. We will give a probability theoretic interpretation to products on the hypergroup. The hypergroup can be identified with a commutative…

In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected.…

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…

A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…