Related papers: Estimating graph parameters with random walks

In this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graph $G$, each pair of vertices are joined by an edge with a probability $p$, where $p$ is a…

For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…

For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the…

Temporal graphs are graphs where the edge set can change in each time step, and the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been…

Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…

We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…

Using random walks for sampling has proven advantageous in assessing the characteristics of large and unknown social networks. Several algorithms based on random walks have been introduced in recent years. In the practical application of…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…

Given an integer $n$, let $G(n)$ be the number of integer sequences $n-1\ge d_1\ge d_2\ge\dotsb\ge d_n\ge 0$ that are the degree sequence of some graph. We show that $G(n)=(c+o(1))4^n/n^{3/4}$ for some constant $c>0$, improving both the…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

Given a connected graph $G$ with some subset of its vertices excited and a fixed target vertex, in the geodesic-biased random walk on $G$, a random walker moves as follows: from an unexcited vertex, she moves to a uniformly random…

We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of…

We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{\rm hit}$, both in terms of the relaxation time. We also prove a…

Given an $n$-vertex $m$-edge graph $G$ with non negative edge-weights, the girth of $G$ is the weight of a shortest cycle in $G$. For any graph $G$ with polynomially bounded integer weights, we present a deterministic algorithm that…

Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…

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…

For random walks on graph $\mathcal{G}$ with $n$ vertices and $m$ edges, the mean hitting time $H_j$ from a vertex chosen from the stationary distribution to vertex $j$ measures the importance for $j$, while the Kemeny constant…

Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…

The random order graph streaming model has received significant attention recently, with problems such as matching size estimation, component counting, and the evaluation of bounded degree constant query testable properties shown to admit…

We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…