Related papers: Random Walks on Hypergraphs with Edge-Dependent Ve…
We prove that the linearly edge reinforced random walk (LRRW) on any graph with bounded degrees is recurrent for sufficiently small initial weights. In contrast, we show that for non-amenable graphs the LRRW is transient for sufficiently…
Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…
We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…
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…
There are a lot of recent works on generalizing the spectral theory of graphs and graph partitioning to hypergraphs. There have been two broad directions toward this goal. One generalizes the notion of graph conductance to hypergraph…
In this article, we develop a theory for understanding the traces left by a random walk in the vicinity of a randomly chosen reference vertex. The analysis is related to interlacements but goes beyond previous research by showing weak limit…
Link partitioning is a popular approach in network science used for discovering overlapping communities by identifying clusters of strongly connected links. Current link partitioning methods are specifically designed for networks modelled…
Recent work in graph models has found that probabilistic hyperedge replacement grammars (HRGs) can be extracted from graphs and used to generate new random graphs with graph properties and substructures close to the original. In this paper,…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
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,…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…
We introduce and study a metapopulation model of random walkers interacting at the nodes of a complex network. The model integrates random relocation moves over the links of the network with local interactions depending on the node…
Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighbourhoods of nodes in hypergraphs. We establish their relationships to lattice…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
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 demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and…