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Quantum walks on networks are a paradigmatic model in quantum information theory. Quantum-walk algorithms have been developed for various applications, including spatial-search problems, element-distinctness problems, and node centrality…
We utilize the PageRank vector to generalize the $k$-means clustering algorithm to directed and undirected graphs. We demonstrate that PageRank and other centrality measures can be used in our setting to robustly compute centrality of nodes…
Centrality measures are used in network science to evaluate the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of…
To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as…
In an era where accumulating data is easy and storing it inexpensive, feature selection plays a central role in helping to reduce the high-dimensionality of huge amounts of otherwise meaningless data. In this paper, we propose a graph-based…
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…
Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large…
Quantum computing has the potential to solve complex problems faster and more efficiently than classical computing. It can achieve speedups by leveraging quantum phenomena like superposition, entanglement, and tunneling. Quantum walks (QWs)…
Centrality metrics play a crucial role in network analysis, while the choice of specific measures significantly influences the accuracy of conclusions as each measure represents a unique concept of node importance. Among over 400 proposed…
Identifying important nodes for disease spreading is a central topic in network epidemiology. We investigate how well the position of a node, characterized by standard network measures, can predict its epidemiological importance in any…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk…
The main results on quantum walk search are scattered over different, incomparable frameworks, most notably the hitting time framework, originally by Szegedy, the electric network framework by Belovs, and the MNRS framework by Magniez,…
We present a novel graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
The mean squared displacement has been widely used as the primary metric for comparing quantum and classical random walks, with quantum walks showing quadratic scaling versus linear scaling for classical walks. However, this comparison may…
The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by…
Quantum walks have wide applications in quantum information, such as universal quantum computation, so it is important to explore properties of quantum walks thoroughly. We propose a novel method to implement discrete-time quantum walks…
There are at least three models of discrete-time quantum walks (QWs) on graphs currently under active development. In this work we focus on the equivalence of two of them, known as Szegedy's and staggered QWs. We give a formal definition of…
Coined Quantum Walks (QWs) are being used in many contexts with the goal of understanding quantum systems and building quantum algorithms for quantum computers. Alternative models such as Szegedy's and continuous-time QWs were proposed…
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…