Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, New Delhi-110025, India.
School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India.
Sci Rep. 2016 Apr 26;6:24926. doi: 10.1038/srep24926.
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws that are signatures of self-organization in complex networks. The modular organization, in terms of modular mass, inter-modular, and intra-modular interaction, also obeys fractal nature. The parameters which characterize topological properties of brain networks follow one parameter scaling theory in all levels of network structure, which reveals the self-similar rules governing the network structure. Further, the calculated fractal dimensions of brain networks of different species are found to decrease when one goes from lower to higher level species which implicates the more ordered and self-organized topography at higher level species. The sparsely distributed hubs in brain networks may be most influencing nodes but their absence may not cause network breakdown, and centrality parameters characterizing them also follow one parameter scaling law indicating self-similar roles of these hubs at different levels of organization in brain networks. The local-community-paradigm decomposition plot and calculated local-community-paradigm-correlation co-efficient of brain networks also shows the evidence for self-organization in these networks.
脑网络的组织表现出高度模块化的特征，模块间的相互作用较弱。网络的拓扑结构涉及到模块和子模块的出现，这些模块和子模块是由分形规律控制的不同组成层次上的自组织的特征，分形规律也是复杂网络自组织的标志。模块组织，无论是在模块质量、模块间还是模块内的相互作用方面，都遵循分形性质。在网络结构的所有层次上，表征脑网络拓扑性质的参数都遵循一个参数标度理论，这揭示了支配网络结构的自相似规则。此外，还发现不同物种的脑网络的计算分形维数从低等物种到高等物种逐渐减小，这表明高等物种的拓扑结构更加有序和自组织。脑网络中稀疏分布的枢纽可能是最具影响力的节点，但它们的缺失不一定会导致网络崩溃，表征它们的中心性参数也遵循一个参数标度律，表明这些枢纽在脑网络不同组织层次上具有自相似的作用。脑网络的局部社区范式分解图和计算的局部社区范式相关系数也为这些网络中的自组织提供了证据。
