Related papers: Ranking nodes in directed networks via continuous-…
Centrality measures identify and rank the most influential entities of complex networks. In this paper, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in…
Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the…
We report results from an experiment on ranking visual markers and node positioning techniques for network visualizations. Inspired by prior ranking studies, we rethink the ranking when the dataset size increases and when the markers are…
We introduce a set of techniques that allow for efficiently generating many independent random walks in the Massive Parallel Computation (MPC) model with space per machine strongly sublinear in the number of vertices. In this…
We address the quantum search of a target node on a cycle graph by means of a quantum walk assisted by continuous measurement and feedback. Unlike previous spatial search approaches, where the oracle is described as a projector on the…
In an interacting continuous time quantum walk, while the walker (the cursor) is moving on a graph, computational primitives (unitary operators associated with the edges) are applied to ancillary qubits (the register). The model with one…
Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it has been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The…
The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in…
Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of…
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves or bound states are obtained, which provide…
Eigenvector centrality is an established measure of global connectivity, from which the importance and influence of nodes can be inferred. We introduce a local eigenvector centrality that incorporates both local and global connectivity.…
We introduce a framework for network analysis based on random walks on directed acyclic graphs where the probability of passing through a given node is the key ingredient. We illustrate its use in evaluating the mutual influence of nodes…
Navigability is a distinctive features of graphs associated with artificial or natural systems whose primary goal is the transportation of information or goods. We say that a graph $\mathcal{G}$ is navigable when an agent is able to…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
The dangling nodes is the nodes with no out-links in the web graph. It saves many computational cost and operations provided the dangling nodes are lumped into one node. In this paper, motivated by so many dangling nodes in web graph, we…
Distributing arbitrary graph states across quantum networks is a central challenge for modular quantum computing and measurement-based quantum communication. We introduce the phase quantum walk (PQW), a discrete-time quantum walk in which…
We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in…
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…
Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…
Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools…