Related papers: Average hitting times in some $f$-equitable graphs
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
We present analytical results for the distribution of first hitting times of random walks (RWs) on random regular graphs (RRGs) of degree $c \ge 3$ and a finite size $N$. Starting from a random initial node at time $t=1$, at each time step…
Let $G$ be a graph. Assume that to each vertex of a set of vertices $S\subseteq V(G)$ a robot is assigned. At each stage one robot can move to a neighbouring vertex. Then $S$ is a mobile general position set of $G$ if there exists a…
We come up with a class of distributed quantized averaging algorithms on asynchronous communication networks with fixed, switching and random topologies. The implementation of these algorithms is subject to the realistic constraint that the…
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e. random graphs…
The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous…
The $k$-th power of the adjacency matrix of a simple undirected graph represents the number of walks with length $k$ between pairs of nodes. As a walk where no node repeats, a path is a walk where each node is only visited once. The set of…
When averages over all starting points are considered, the Type Problem for the recurrence or transience of a simple random walk on an inhomogeneous network in general differs from the usual "local" Type Problem. This difference leads to a…
Temporal graphs (in which edges are active at specified times) are of particular relevance for spreading processes on graphs, e.g.~the spread of disease or dissemination of information. Motivated by real-world applications, modification of…
This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact averaging) and their use in Gradient Tracking. We provide an…
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In this…
We revisit the problem of estimates of moments of random n-dimensional matrices of Wigner ensemble by using the approach elaborated by Ya. Sinai and A. Soshnikov and further developed by A. Ruzmaikina. Our main subject is given by the…
We prove a refined version of the Aldous and Brown's exponential approximation of stationary hitting times. These are valid for all reversible Markov chains. We then specialise our estimates for vertex-transitive graphs, where we obtain…
Let $X$ be a graph with adjacency matrix $A$. The \textsl{continuous quantum walk} on $X$ is determined by the unitary matrices $U(t)=\exp(itA)$. If $X$ is the complete graph $K_n$ and $a\in V(X)$, then \[1-|U(t)_{a,a}|\le2/n. \] In a…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph $G$ with the integer lattice, seen as a…
We present a general framework, applicable to a broad class of random walks on complex networks, which provides a rigorous lower bound for the mean first-passage time of a random walker to a target site averaged over its starting position,…
We study the set of probability distributions visited by a continuous-time quantum walk on graphs. An edge-weighted graph G is universal mixing if the instantaneous or average probability distribution of the quantum walk on G ranges over…