Related papers: Scalable and Provable Kemeny Constant Computation …

Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…

We give new general formulas for the asymptotics of the number of spanning trees of a large graph. A special case answers a question of McKay (1983) for regular graphs. The general answer involves a quantity for infinite graphs that we call…

Random walks can reveal communities or clusters in networks, because they are more likely to stay within a cluster than leave it. Thus, one family of community detection algorithms uses random walks to measure distance between pairs of…

With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi-labeled…

The forest matrix plays a crucial role in network science, opinion dynamics, and machine learning, offering deep insights into the structure of and dynamics on networks. In this paper, we study the problem of querying entries of the forest…

Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…

Analyzing social graphs with limited data access is challenging for third-party researchers. To address this challenge, a number of algorithms that estimate structural properties via a random walk have been developed. However, most existing…

Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…

We study random two-dimensional spanning forests in the plane that can be viewed both in the discrete case and in their appropriately taken scaling limits as a uniformly chosen spanning tree with some Poissonian deletion of edges or points.…

This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…

Random walk-based sampling methods are gaining popularity and importance in characterizing large networks. While powerful, they suffer from the slow mixing problem when the graph is loosely connected, which results in poor estimation…

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…

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…

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…

Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…

We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the variance of hitting times. For a simple random walk on a…

Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a…

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…

In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…

We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations,…