Are networks with more edges easier to synchronize,or not? |
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引用本文: | 段志生,王文旭,刘超,陈关荣.Are networks with more edges easier to synchronize,or not?[J].中国物理 B,2009,18(8):3122-3130. |
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作者姓名: | 段志生 王文旭 刘超 陈关荣 |
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作者单位: | State Key Laboratory for Turbulence and Complex
Systems, Department of Mechanics and Aerospace Engineering,
College of
Engineering, Peking University, Beijing 100871, China;Department of Electronic Engineering, City University of
Hong Kong, Hong Kong, China;State Key Laboratory for Turbulence and Complex
Systems, Department of Mechanics and Aerospace Engineering,
College of
Engineering, Peking University, Beijing 100871, China;State Key Laboratory for Turbulence and Complex
Systems, Department of Mechanics and Aerospace Engineering,
College of
Engineering, Peking University, Beijing 100871, China;Department of Electronic Engineering, City University of
Hong Kong, Hong Kong, C |
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基金项目: | Project
supported by the National Natural Science Foundation of China (Grant
Nos 10832006 and 60674093), the Foundation for Key Program of
Educational Ministry, China (Grant No 107110) and the City
University of Hong Kong under the Research Enhancement
Scheme and SRG (Grant No 9041335). |
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摘 要: | In this paper, the relationship between network
synchronizability and the edge-addition of its associated graph is
investigated. First, it is shown that adding one edge to a cycle
definitely decreases the network synchronizability. Then, since
sometimes the synchronizability can be enhanced by changing the
network structure, the question of whether the networks with more
edges are easier to synchronize is addressed. Based on a subgraph
and complementary graph method, it is shown by examples that the
answer is negative even if the network structure is arbitrarily
optimized. This reveals that generally there are redundant edges in
a network, which not only make no contributions to synchronization
but actually may reduce the synchronizability. Moreover, a simple
example shows that the node betweenness centrality is not always a
good indicator for the network synchronizability. Finally, some more
examples are presented to illustrate how the network
synchronizability varies following the addition of edges, where all
the examples show that the network synchronizability globally
increases but locally fluctuates as the number of added edges
increases.
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关 键 词: | complex network complementary graph synchronizability edge addition |
收稿时间: | 2008-09-15 |
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