标题： 分层社区通过一般自组织原理形成的普遍自相似性 显示英文标题

标题： Universal self-similarity of hierarchical communities formed through a general self-organizing principle

摘要： 分层社区结构中自相似性的出现是复杂系统中的普遍现象。 然而，缺乏描述此类结构形成的通用量化方法和一般原理。 在这里，我们发现多个现实世界网络中描述自相似分层社区结构的尺度定律具有普遍性，包括生物、基础设施和社会网络。 我们使用一个现象学模型复制了这些尺度关系，其中属性相似性更高的节点形成连接的概率更大。 它们属性的较大差异迫使两个节点进入不同的社区。 由于较大社区内节点属性的进一步差异，形成了较小的社区。 我们发现一般的自组织原则与哈肯原理一致；节点自我组织成群体，使得同一社区中节点的多样性或差异在每个尺度上最小化，并且随着组织结构复杂性的增加，组织熵减少。 显示英文摘要

摘要： Emergence of self-similarity in hierarchical community structures is ubiquitous in complex systems. Yet, there is a dearth of universal quantification and general principles describing the formation of such structures. Here, we discover universality in scaling laws describing self-similar hierarchical community structure in multiple real-world networks including biological, infrastructural, and social networks. We replicate these scaling relations using a phenomenological model, where nodes with higher similarity in their properties have greater probability of forming a connection. A large difference in their properties forces two nodes into different communities. Smaller communities are formed owing to further differences in node properties within a larger community. We discover that the general self-organizing principle is in agreement with Hakens principle; nodes self-organize into groups such that the diversity or differences between properties of nodes in the same community is minimized at each scale and the organizational entropy decreases with increasing complexity of the organized structure.