Graphicality conditions for general scale-free complex networks and their application to visibility graphs

Rodríguez, Miguel A.

doi:10.1103/physreve.94.012314

Cited by 5 publications

(6 citation statements)

References 16 publications

(42 reference statements)

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“…erefore, when sampling a bipartite network with power-law distributions, one needs to consider the constraint k i ≡ d i . One more thing is that one needs to consider the graphicality condition [98] when sampling multipartite networks with power-law degree distributions. How to sample multipartite networks with arbitrary degree distributions is also challenging and deserves further in-depth dedications [99][100][101].…”

Section: Discussionmentioning

confidence: 99%

Interdependency and Vulnerability of Multipartite Networks under Target Node Attacks

2019

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Complex networks in reality may su er from target attacks which can trigger the breakdown of the entire network. It is therefore pivotal to evaluate the extent to which a network could withstand perturbations. e research on network robustness has proven as a potent instrument towards that purpose. e last two decades have witnessed the enthusiasm on the studies of network robustness. However, existing studies on network robustness mainly focus on multilayer networks while little attention is paid to multipartite networks which are an indispensable part of complex networks. In this study, we investigate the robustness of multipartite networks under intentional node attacks. We develop two network models based on the largest connected component theory to depict the cascading failures on multipartite networks under target attacks. We then investigate the robustness of computer-generated multipartite networks with respect to eight node centrality metrics. We discover that the robustness of multipartite networks could display either discontinuous or continuous phase transitions. Interestingly, we discover that larger number of partite sets of a multipartite network could increase its robustness which is opposite to the phenomenon observed on multilayer networks. Our ndings shed new lights on the robust structure design of complex systems. We nally present useful discussions on the applications of existing percolation theories that are well studied for network robustness analysis to multipartite networks. We show that existing percolation theories are not amenable to multipartite networks. Percolation on multipartite networks still deserves in-depth e orts.

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Section: Discussionmentioning

confidence: 99%

Interdependency and Vulnerability of Multipartite Networks under Target Node Attacks

2019

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“…For generic scale-free networks, this condition reads κ < 1/γ in the range 1 < γ < 2. The constraints imposed by graphical conditions in visibility networks have been treated in [17]. It is worth remarking that these constraints apply to networks whose degree distributions exhibit true power laws without size dependence.…”

Section: Large-scale Structure Of Complex Networkmentioning

confidence: 99%

“…On the one hand, let us consider the scaling of the maximum degree with the system size through the exponent κ as k M ∼ N κ . As mentioned in [17], κ is in fact the fractal dimension of the visible sites from the site of maximum visibility. Given the self-affine property of the series in the SA class, a close connection between the exponents α = α loc and this fractal dimension can be expected.…”

Section: A Time Series With One Spectral Scale: Sa and Sn Classesmentioning

confidence: 99%

Relating the large-scale structure of time series and visibility networks

Rodríguez

2017

Phys. Rev. E

Self Cite

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The structure of time series is usually characterized by means of correlations. A new proposal based on visibility networks has been considered recently. Visibility networks are complex networks mapped from surfaces or time series using visibility properties. The structures of time series and visibility networks are closely related, as shown by means of fractional time series in recent works. In these works, a simple relationship between the Hurst exponent H of fractional time series and the exponent of the distribution of edges γ of the corresponding visibility network, which exhibits a power law, is shown. To check and generalize these results, in this paper we delve into this idea of connected structures by defining both structures more properly. In addition to the exponents used before, H and γ, which take into account local properties, we consider two more exponents that, as we will show, characterize global properties. These are the exponent α for time series, which gives the scaling of the variance with the size as var∼T^{2α}, and the exponent κ of their corresponding network, which gives the scaling of the averaged maximum of the number of edges, 〈k_{M}〉∼N^{κ}. With this representation, a more precise connection between the structures of general time series and their associated visibility network is achieved. Similarities and differences are more clearly established, and new scaling forms of complex networks appear in agreement with their respective classes of time series.

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“…However, at present, in the field of software engineering, there is little research on the software network motif, especially the open source operating system software package network motif, and it has not yet been applied in the process of version evolution analysis. Therefore, this paper investigates open source operating system evolution from the perspective of the package dependency network motif for the sake of discovering potential cooperation and reusing schema in software development [4,9,[14][15][16][17][18][19][20]. Specifically, this manuscript makes three main contributions:…”

Section: Introductionmentioning

confidence: 99%

Analysis of Open Source Operating System Evolution: A Perspective from Package Dependency Network Motif

Wang

Tan

et al. 2019

Symmetry

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Complexity of open source operating systems constantly increase on account of their widespread application. It is increasingly difficult to understand the collaboration between components in the system. Extant research of open source operating system evolution is mainly achieved by Lehman’s law, which is conducted by analyzing characteristics such as line of the source code. Networks, which are utilized to demonstrate relationships among entities, is an adequate model for exploring cooperation of units that form a software system. Software network has become a research hotspot in the field of software engineering, leading to a new viewpoint for us to estimate evolution of open source operating systems. Motif, a connected subgraph that occurs frequently in a network, is extensively used in other scientific research such as bioscience to detect evolutionary rules. Thus, this paper constructs software package dependency network of open source software operating systems and investigates their evolutionary discipline from the perspective of the motif. Results of our experiments, which took Ubuntu Kylin as a study example, indicate a stable evolution of motif change as well as discovering structural defect in that system.

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Graphicality conditions for general scale-free complex networks and their application to visibility graphs

Cited by 5 publications

References 16 publications

Interdependency and Vulnerability of Multipartite Networks under Target Node Attacks

Interdependency and Vulnerability of Multipartite Networks under Target Node Attacks

Relating the large-scale structure of time series and visibility networks

Analysis of Open Source Operating System Evolution: A Perspective from Package Dependency Network Motif

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