Quantum Google in a Complex Network

Paparo, Giuseppe Davide; Müller, Markus; Comellas, Francesc; Martín-Delgado, M. A.

doi:10.1038/srep02773

Cited by 92 publications

(148 citation statements)

References 68 publications

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“…In fact, both quantities have been already used to characterize the eigenfunctions of the adjacency matrices of random network models (see some examples in Refs. [31,36,39,42,48,[53][54][55][56][57][66][67][68][69]). …”

Section: B Entropic Eigenfunction Localization Lengthmentioning

confidence: 99%

Universality in the spectral and eigenfunction properties of random networks

et al. 2015

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By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution P (s) and the entropic eigenfunction localization length of the adjacency matrices of Erdős-Rényi (ER) fully random networks are universal for fixed average degree ξ ≡ αN (α and N being the average network connectivity and the network size, respectively). We also demonstrate that Brody distribution characterizes well P (s) in the transition from α = 0, when the vertices in the network are isolated, to α = 1, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks.

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Section: B Entropic Eigenfunction Localization Lengthmentioning

confidence: 99%

Universality in the spectral and eigenfunction properties of random networks

et al. 2015

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“…In this article, we largely follow the analysis in [7], but extend it in three ways. Firstly, we consider the time-scale involved for discrete-time-quantum-walk-based PageRank.…”

Section: Introductionmentioning

confidence: 99%

“…In [7], Paparo et al performed further analysis of their proposed quantum PageRank on complex networks, specifically on hierarchical graphs, directed scale-free graphs, and Erdös-Rényi random graphs. The quantum PageRank algorithm not only distinguished clearly between the three graph classes, but also exhibited distinct characteristics in terms of highlighting secondary hubs and lifting the degeneracy of low-lying nodes.…”

Section: Introductionmentioning

confidence: 99%

“…Similar to the discrete-time case, the open-system PageRank lifted classical rank degeneracy of lowly connected nodes, whilst preserving identification of the most central nodes. By extension, it is useful to ascertain whether the other characteristics found in [7] for the discrete-time quantum PageRank are reflected in the open-system scheme.…”

Section: Introductionmentioning

confidence: 99%

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Comparing classical and quantum PageRanks

Loke

Tang

Rodriguez

et al. 2016

Quantum Inf Process

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Following recent developments in quantum PageRanking, we present a comparative analysis of discrete-time and continuous-time quantum-walk-based PageRank algorithms. For the discrete-time case, we introduce an alternative PageRank measure based on the maximum probabilities achieved by the walker on the nodes. We demonstrate that the required time of evolution does not scale significantly with increasing network size. We affirm that all three quantum PageRank measures considered here distinguish clearly between outerplanar hierarchical, scale-free, and Erdös-Rényi network types. Relative to classical PageRank and to different extents, the quantum measures better highlight secondary hubs and resolve ranking degeneracy among peripheral nodes for the networks we studied in this paper.

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“…There are many realistic systems which can be described in terms of complex networks in nature and society [5], such as online social networks [6,7], protein-protein interaction networks [8], the Internet [9,10], and transportation networks [11,12]; therefore, a wide range of specialists have paid considerable attention to the topology structure characteristics of complex networks.…”

Section: Introductionmentioning

confidence: 99%

Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure

Zhao

2017

Int. J. Onl. Eng.

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Abstract-For real-world wireless sensor networks (WSNs), the invulnerability of the network is very critical, because a cascading failure would cause a serious effect on the whole network performance. Network survivability is closely dependent on the topology structure of a network. In this paper, [Note: If you use "firstly," you need to add "secondly," "thirdly,"... "finally" throughout this paragraph; I don't see a need for this here] we meticulously study the topology characteristics of WSNs based on the complex network theory. According to scale-free and small-world features of complex networks, the nodes of WSNs are divided into different types, including common node, super node, and sink node. From the point of view of invulnerability in complex networks, the influence of different types of nodes on the sensor networks' invulnerability is analyzed. Simulation experiments show that adding super nodes to the WSNs would significantly improve network survivability.

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Quantum Google in a Complex Network

Cited by 92 publications

References 68 publications

Universality in the spectral and eigenfunction properties of random networks

Universality in the spectral and eigenfunction properties of random networks

Comparing classical and quantum PageRanks

Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure

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