标题： 具有分层组织的模块化网络：复杂结构的动力学影响 显示英文标题

标题： Modular networks with hierarchical organization: The dynamical implications of complex structure

摘要： 许多在现实生活中出现的网络具有以分层方式排列的模块化结构。 在本文中，我们提出了一种此类网络的模型，使用了随机生成方法。 利用这个模型，我们表明，节点的聚类与度之间的标度关系并不是分层模块化网络的必要属性，这与之前基于确定性构建模型的建议相反。 我们还研究了此类网络上的动态过程，特别是网络动态的平衡点稳定性和网络中的同步活动。 对于这两种情况，我们发现，增加模块性或分层级别往往会增加不稳定的概率。 由于层次结构和模块性在自然系统中都被观察到，而这些系统必须对环境波动具有鲁棒性，因此我们得出结论，为了分层结构的出现需要额外的约束条件，类似于我们之前通过多约束优化展示的模块性的出现。 显示英文摘要

摘要： Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that, the scaling relation between the clustering and degree of the nodes is not a necessary property of hierarchical modular networks, as had previously been suggested on the basis of a deterministically constructed model. We also look at dynamics on such networks, in particular, the stability of equilibria of network dynamics and of synchronized activity in the network. For both of these, we find that, increasing modularity or the number of hierarchical levels tends to increase the probability of instability. As both hierarchy and modularity are seen in natural systems, which necessarily have to be robust against environmental fluctuations, we conclude that additional constraints are necessary for the emergence of hierarchical structure, similar to the occurrence of modularity through multi-constraint optimization as shown by us previously.