Eguíluz Víctor M, Pérez Toni, Borge-Holthoefer Javier, Arenas Alex
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), E-07122 Palma de Mallorca, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056113. doi: 10.1103/PhysRevE.83.056113. Epub 2011 May 19.
Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology γ is related to the exponent of the associated functional network as α=(2-γ)(-1) for γ<2.
复杂系统的功能网络是通过对其组成部分的时间活动进行分析而获得的，并且经常用于推断其未知的潜在连通性。我们得到了复杂网络中扩散延迟耦合元件系统中拓扑与功能之间的关系方程。我们精确求解了基序（三个节点的有向结构）和有向网络中的所得方程。有向不相关网络的平均场解表明，活动的聚类由节点的入度主导，并且锁定频率随着平均度的增加而降低。我们发现，对于γ<2，结构拓扑的幂律度分布指数γ与相关功能网络的指数α的关系为α=(2-γ)(-1)。
