2014 Fiscal Year Final Research Report
Construction of a general theory of percolation on complex networks with strong degree-degree correlation
| Project/Area Number |
24540419
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kochi National College of Technology |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 複雑ネットワーク / 数理物理 / 物性基礎論 / 高信頼ネットワーク / セキュア・ネットワーク / 相転移理論 |
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| Outline of Final Research Achievements |
The purpose of this research was to construct a general theory applicable to percolation on complex networks with strong degree-degree correlation. The research was conducted according to the proposed plan, and I obtained following three main results: (i) The optimal network structure against malicious targeted attack was derived analytically, which is hierarchically interconnected random regular graphs and now commonly referred to as the "onion structure." This structure has the maximum positive degree correlation. (ii) It was numerically confirmed that the particle diffusion on networks with negative degree correlation is much faster than on networks with positive correlation. (iii) A general form of generating function of a system of interconnected complex networks with arbitrary degree correlation was derived and a general theoretical framework of percolation on interconnected complex networks was constructed, which fulfills the purpose of this research project.
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| Free Research Field |
物性理論
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