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摘要: 链路预测是研究复杂网络结构演化趋势的重要组成部分, 用于预测网络丢失的连边和未来可能出现的连边, 具有极大的理论和应用价值.当前链路预测研究成果主要基于网络结构特征对连边进行预测, 具体分析其连边机理的研究较少.网络同步的研究能够深刻反映节点的动力学演化行为与网络结构之间的内在机理.本文针对链路预测考虑的静态网络引入节点动力学模型构成动态网络, 通过分析链路预测连边与动态网络模型同步之间的关系, 对链路预测连边机理进行分析研究.通过实验与理论分析总结发现了链路预测连边具有同步能力稳定性的规律.进一步讨论了链路预测连边的动力学机理, 并揭示了链路预测连边机理与真实网络演化的差别.Abstract: Link prediction is an important part of the study of the evolutionary trend of complex network structure. It is used to predict the missing links and future links of network, and has great theoretical and practical value. The current link prediction researches are mainly based on the characteristics of the network structure. The study of network synchronization can profoundly reflect the internal mechanism between the node's dynamic evolution behavior and network structure. In this paper, we introduce a node dynamic model for link prediction research. By analyzing the relationship between the link prediction and the synchronization of the dynamic network model, we analyze the link prediction mechanism. Furthermore, we discuss the dynamic mechanism of link prediction, and reveal the difference between link prediction mechanism and real network evolution.
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Key words:
- Complex network /
- link prediction /
- synchronization /
- master stability function
1) 本文责任编委 陈积明 -
表 1 网络的拓扑特征参数
Table 1 Topological characteristic parameters of the network
网络 $ N$ $M$ $k $ $ L $ $C $ Jazz 198 2 742 27.697 2.235 0.6175 USair 332 2 126 12.807 2.738 0.6252 PB 1 222 16 714 27.355 2.738 0.3203 Yeast 2 375 11 693 9.848 5.096 0.3057 FWFB 128 2 075 32.422 1.776 0.3346 
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表 2 演化网络同步能力增长率(%)
Table 2 Growth rate of evolutionary network synchronizability (%)
$G_{\rm CN}$ $G_{AA}$ $G_{\rm PA}$ $G_{\rm Katz}$ $G_{\rm rd}$ NW 2.74 2.98 1.92 2.51 19.95 Jazz 0.09 0.10 0.51 0.07 402.73 USair 0.04 0.04 0.45 0.04 599.47 PB 0 0 0 0 183.85 Yeast 0 0 0.01 0 1 277.52 FWEB 0 0 0.27 0.08 491.64
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表 3 CN演化网络同步能力增长率(%)
Table 3 Growth rate of CN evolutionary network synchronizability (%)
1 2 3 5 7 10 NW 0.11 0.22 0.31 0.82 1.03 2.74 Jazz 0 0 0.02 0.04 0.07 0.09 USair 0 0 0 0.01 0.02 0.04 PB 0 0 0 0 0 0 Yeast 0 0 0 0 0 0 FWEB 0 0 0 0 0 0
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表 4 AA演化网络同步能力增长率(%)
Table 4 Growth rate of AA evolutionary network synchronizability (%)
1 2 3 5 7 10 NW 0.10 0.23 0.30 0.93 1.34 2.98 Jazz 0 0 0.02 0.05 0.08 0.10 USair 0 0 0 0 0.02 0.04 PB 0 0 0 0 0 0 Yeast 0 0 0 0 0 0 FWEB 0 0 0 0 0 0
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表 5 PA演化网络同步能力增长率(%)
Table 5 Growth rate of PA evolutionary network synchronizability (%)
1 2 3 5 7 10 NW 0.07 0.29 0.31 0.72 1.06 1.92 Jazz 0.09 0.10 0.13 0.21 0.42 0.51 USair 0.03 0.04 0.06 0.20 0.32 0.45 PB 0 0 0 0 0 0 Yeast 0 0 0 0 0 0.01 FWEB 0 0 0 0.05 0.12 0.27
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表 6 Katz演化网络同步能力增长率(%)
Table 6 Growth rate of Katz evolutionary network synchronizability (%)
1 2 3 5 7 10 NW 0.15 0.32 0.39 0.94 1.12 2.51 Jazz 0 0 0.02 0.04 0.06 0.07 USair 0 0 0 0.01 0.02 0.04 PB 0 0 0 0 0 0 Yeast 0 0 0 0 0 0 FWEB 0 0 0 0 0.03 0.08
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