Related papers: Centrality measure based on continuous-time quantu…

Multilayer network analysis is a useful approach for studying the structural properties of entities with diverse, multitudinous relations. Classifying the importance of nodes and node-layer tuples is an important aspect of the study of…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…

Here we present a range-limited approach to centrality measures in both non-weighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on…

Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…

In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…

Most previous work of centralities focuses on metrics of vertex importance and methods for identifying powerful vertices, while related work for edges is much lesser, especially for weighted networks, due to the computational challenge. In…

Vertices with high betweenness and closeness centrality represent influential entities in a network. An important problem for time varying networks is to know a-priori, using minimal computation, whether the influential vertices of the…

Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…

The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…

Herein we present a novel approach of identifying community structures in complex networks. We propose the usage of the Random Walk Centrality (RWC), first introduced by Noh and Rieger [Phys. Rev. Lett. 92.11 (2004): 118701]. We adapt this…

We introduce a new measure of centrality, the information centrality C^I, based on the concept of efficient propagation of information over the network. C^I is defined for both valued and non-valued graphs, and applies to groups and classes…

Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…

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…

We develop efficient and effective strategies for the update of Katz centralities after node and edge removal in simple graphs. We provide explicit formulas for the ``loss of walks" a network suffers when nodes/edges are removed, and use…

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…

Structure of real networked systems, such as social relationship, can be modeled as temporal networks in which each edge appears only at the prescribed time. Understanding the structure of temporal networks requires quantifying the…