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Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…
Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the…
This paper presents a nested tracking framework for analyzing cycles in 2D force networks within granular materials. These materials are composed of interacting particles, whose interactions are described by a force network. Understanding…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking…
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…
The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…
Locally Markov walks are natural generalizations of classical Markov chains, where instead of a particle moving independently of the past, it decides where to move next depending on the last action performed at the current location. We…
We give three different criteria for transience of a Branching Markov Chain. These conditions enable us to give a classification of Branching Random Walks in Random Environment (BRWRE) on Cayley Graphs in recurrence and transience. This…
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…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…
The sheer increase in the size of graph data has created a lot of interest into developing efficient distributed graph processing frameworks. Popular existing frameworks such as Graphlab and Pregel rely on balanced graph partitioning in…
Discriminative Random Walks (DRWs) are a simple yet powerful tool for semi-supervised node classification, but their theoretical foundations remain fragmentary. We revisit DRWs through the lens of information geometry, treating the family…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
We present a new statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to…
This article introduces a concept and measure of graph compartmentalization. This new measure allows for principled comparison between graphs of arbitrary structure, unlike existing measures such as graph modularity. The proposed measure is…
Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper marks the initial stride toward achieving this…
We consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of…
Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null…