Related papers: Random Walks on Simplicial Complexes and the norma…
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…
The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial…
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite 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…
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on…
We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph $G$, a positive integer $r$, and a set $S$ of vertices, approximates the conductance of $S$ in the $r$-step random walk on $G$ to within a factor of…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
The eigenvalues of the normalized Laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects, specifically in relation to random walks. In this paper we determine…
We consider the Dyson hierarchical graph $\mathcal{G}$, that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter $\sigma \in (1/2, 1]$. Exploiting the deterministic recursivity through which…
In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…
Web-based interactions can be frequently represented by an attributed graph, and node clustering in such graphs has received much attention lately. Multiple efforts have successfully applied Graph Convolutional Networks (GCN), though with…
In this paper we derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the uniform multicommodity flow problem under random walk routing. We show the mean load is linearly dependent on the nodal…
We study random walks on dynamically evolving graphs, where the environment is given by a time-dependent subset of the edges of an underlying graph. Concretely, following the recently introduced framework of Lelli and Stauffer, we consider…
Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…
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…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
Networks and network processes have emerged as powerful tools for modeling social interactions, disease propagation, and a variety of additional dynamics driven by relational structures. Recently, neural networks have been generalized to…
The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems,…