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A unified framework for equivalences in social networks
arXiv - CS - Discrete Mathematics Pub Date : 2020-06-18 , DOI: arxiv-2006.10733
Nina Otter and Mason A. Porter

A key concern in network analysis is the study of social positions and roles of actors in a network. The notion of "position" refers to an equivalence class of nodes that have similar ties to other nodes, whereas a "role" is an equivalence class of compound relations that connect the same pairs of nodes. An open question in network science is whether it is possible to simultaneously perform role and positional analysis. Motivated by the principle of functoriality in category theory we propose a new method that allows to tie role and positional analysis together. We illustrate our methods on two well-studied data sets in network science.

中文翻译:

社交网络中等价的统一框架

网络分析的一个关键问题是研究网络中参与者的社会地位和角色。“位置”的概念是指与其他节点具有相似联系的节点的等价类,而“角色”是连接相同节点对的复合关系的等价类。网络科学中的一个悬而未决的问题是是否可以同时进行角色和位置分析。受范畴论中的函子性原则的启发,我们提出了一种新方法,可以将角色和位置分析结合在一起。我们在网络科学中经过充分研究的两个数据集上说明了我们的方法。
更新日期:2020-06-19
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