Generating global network structures by triad types

This paper addresses the question of whether one can generate networks with a given global structure (defined by selected blockmodels, i.e., cohesive, core-periphery, hierarchical, and transitivity), considering only different types of triads. Two methods are used to generate networks: (i) the newly proposed method of relocating links; and (ii) the Monte Carlo Multi Chain algorithm implemented in the ergm package in R. Most of the selected blockmodel types can be generated by considering all types of triads. The selection of only a subset of triads can improve the generated networks’ blockmodel structure. Yet, in the case of a hierarchical blockmodel without complete blocks on the diagonal, additional local structures are needed to achieve the desired global structure of generated networks. This shows that blockmodels can emerge based only on local processes that do not take attributes into account.

本文探讨了这样一项研究问题：仅基于不同类型的三元组（triad），能否生成具有给定全局结构的网络——该全局结构由选定的块模型（blockmodel）定义，包括内聚型、核心-外围型、层级型以及传递型四类。本研究采用两种方法生成网络：其一为新近提出的链路重定位法；其二为在R语言ergm包中实现的蒙特卡洛多链算法（Monte Carlo Multi Chain algorithm）。多数选定的块模型类型可通过考量所有类型的三元组得以生成。仅选取部分三元组子集，能够优化生成网络的块模型结构。然而针对对角线上不含完整块的层级型块模型，还需引入额外的局部结构，方可使生成网络达成预期的全局结构。这一结果表明，块模型可仅通过不考虑节点属性的局部过程自发涌现。