2006 Fiscal Year Final Research Report Summary
Study on Structure and Efficiency Optimization of Complex Networks
| Project/Area Number |
17540367
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
TANIZAKI Toshihiro Kochi National College of Technology, Department of Electrical Engineering, Associate Professor, 電気工学科, 助教授 (60311106)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Basic Physics / Statistical Physics / Network Theory / Optimization of Robustness / System Analysis |
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| Research Abstract |
Year 2005
We have extended the basic theory on the optimization of robustness of complex networks against various types of node removal that we had already developed in the year 2004. In this extension of the theory, we include the optimization of the network robustness against "waves of attacks" on networks, which means repeated selected removal of nodes with possible malfunction of nodes that occurs randomly. This type of attack can happen to network in the real world. We study this problem by an analytical method using exact formula for the node removal threshold. We quantitatively identify the optimal network structure in this case, which has an bimodal structure in the degree distribution of nodes.
Year 2006
In order to understand the relation between the bimodal network structure, which is optimally robust against BOTH random and selective node removal, and the scale-free network, which is robust against random failure but unbelievably fragile against selective node removal, we propose the multi-modal network structure. By increasing the mode number, we can study the transition from the bimodal structure to the scale-free structure continuously. Our results are summarized as follows : (1) we identify the controlling parameter that consists of the total node number and the mode number and governs the node removal thresholds, (2) we numerically calculate the critical mode number at which the robustness against selective node removal, which is the order of the logarithm of the total node number, (3) we numerically estimate the optimal values of the exponent in the power-law degree distribution in the multi-modal network structure. The optimal values fall within the range of 2.5 and 3 that are frequently found in the scale-free networks in the real world.
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