In this paper we investigate phenomena of spontaneous emergence or purposeful formation of highly organized structures in networks of related agents. We show that the formation of large organized structures requires exponentially large, in the size of the structures, networks. Our approach is based on Kolmogorov, or descriptional, complexity of networks viewed as finite size strings. We apply this approach to the study of the emergence or formation of simple organized, hierarchical, structures based on Sierpinski Graphs and we prove a Ramsey type theorem that bounds the number of vertices in Kolmogorov random graphs that contain Sierpinski Graphs as subgraphs. Moreover, we show that Sierpinski Graphs encompass close-knit relationships among their vertices that facilitate fast spread and learning of information when agents in their vertices are engaged in pairwise interactions modelled as two person games. Finally, we generalize our findings for any organized structure with succinct representations. Our work can be deployed, in particular, to study problems related to the security of networks by identifying conditions which enable or forbid the formation of sufficiently large insider subnetworks with malicious common goal to overtake the network or cause disruption of its operation.

翻译：本文研究了关联智能体网络中高度组织化结构的自发涌现或有目的形成现象。我们证明，大规模组织化结构的形成需要网络规模随结构尺寸呈指数级增长。该方法基于将网络视为有限长度字符串的柯尔莫哥洛夫（描述复杂性）度量。我们将此方法应用于基于谢尔宾斯基图的简单组织化层次结构的涌现与形成研究，并证明了一个拉姆齐型定理——该定理界定了包含谢尔宾斯基图作为子图的柯尔莫哥洛夫随机图的顶点数量上限。进一步地，我们证明谢尔宾斯基图顶点间存在紧密关联关系，当顶点上的智能体参与以双人博弈建模的成对交互时，这种关系能促进信息的快速传播与学习。最后，我们将结论推广至任何具有简洁表示的组织化结构。我们的工作可特别部署于网络安全问题研究，通过识别促成或抑制足够大规模恶意内部子网（具有接管网络或破坏其运行的共同目标）形成的条件，为相关分析提供支持。