分析了复杂网络的集聚系数和度分布的异质性这两个重要的描述复杂网络结构特点的特征量对复杂度的影响。研究发现,增大集聚系数能增大复杂度的最大值以及增大复杂度钟形曲线的宽度,而增大度分布的异质性不能增大复杂度的最大值却可以明显增大复杂度在上升段和下降段的取值。对于小世界网络集聚系数对复杂度的影响更明显,而对于无标度网络,度分布的异质性更能显著的改变复杂度的取值。进一步加深了人们对描述网络部分同步状态的复杂度的认识,为设计合理的网络结构提供了理论基础。
Complexity is defined to describe the partial synchronization state in complex networks, which is sensitive to the network structure, however, how the structure affects the complexity is still unclear. Clustering coefficient and degree distribution are two typical parameters in complex networks. In this paper, the effects of these two parameters on complexity are studied. After careful study it is found that increasing clustering coefficient would increase the maximal complexity and broaden the width of the complexity curves, and increasing the heterogeneity of the degree distribution will increase the value of rising and falling part of complexity curve but have no effect on the maximal complexity. Furthermore, complexity is sensitive to clustering coefficient in small-world networks and sensitive to heterogeneity of degree distribution in scale-free networks. Our work deepens the knowledge of complexity, and provide useful theory to design complex network structure.
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