Related papers: A Theory for Backtrack-Downweighted Walks
Document networks are found in various collections of real-world data, such as citation networks, hyperlinked web pages, and online social networks. A large number of generative models have been proposed because they offer intuitive and…
We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex. Three distinct types of…
Hypergraph has been selected as a powerful candidate for characterizing higher-order networks and has received increasing attention in recent years. In this article, we study random walks with resetting on hypergraph by utilizing spectral…
Let ${\cal T}$ be a rooted Galton-Watson tree with offspring distribution $\{p_k\}$ that has $p_0=0$, mean $m=\sum kp_k>1$ and exponential tails. Consider the $\lambda$-biased random walk $\{X_n\}_{n\geq 0}$ on ${\cal T}$; this is the…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…
The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however…
Node embedding is a powerful approach for representing the structural role of each node in a graph. $\textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
It is known that a random walk on $\Z^d$ among i.i.d. uniformly elliptic random bond conductances verifies a central limit theorem. It is also known that approximations of the covariance matrix can be obtained by considering periodic…
Random walks are at the heart of many existing deep learning algorithms for graph data. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to…
We first present a comprehensive review of various random walk metrics used in the literature and express them in a consistent framework. We then introduce fundamental tensor -- a generalization of the well-known fundamental matrix -- and…
Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…
The study of social networks is a burgeoning research area. However, most existing work deals with networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive ("like",…
In this work we consider two different aspects of weighted walks in cones. To begin we examine a particular weighted model, known as the Gouyou-Beauchamps model. Using the theory of analytic combinatorics in several variables we obtain the…
We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…
We propose an experimental mathematics approach leading to the computer-driven discovery of various structural properties of general counting functions coming from enumeration of walks.
We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering…