Coalgebraic analysis of social systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911475298205696 |
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| author | Motamed, Nima Otter, Nina Roff, Emily |
| author_facet | Motamed, Nima Otter, Nina Roff, Emily |
| contents | The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these are methods to determine the roles that exist within a given system, and the positions. The analysis of roles and positions is highly developed for social systems that involve only pairwise interactions among actors - however, in contemporary social network analysis it is increasingly common to use models that can take into account higher-order interactions as well. In this paper we take a category-theoretic approach to the question of how to lift role and positional analysis from graphs to hypergraphs, which can accommodate higher-order interactions. We use the framework of universal coalgebra - a 'theory of systems' with origins in computer science and logic - to formalize the main concepts of role and positional analysis and extend them to a large class of structures that includes both graphs and hypergraphs. As evidence for the validity of our definitions, we prove a very general functoriality theorem that specializes, in the case of graphs, to a folkloric observation about the compatibility of positional and role analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23211 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coalgebraic analysis of social systems Motamed, Nima Otter, Nina Roff, Emily Social and Information Networks Discrete Mathematics Symbolic Computation Category Theory The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these are methods to determine the roles that exist within a given system, and the positions. The analysis of roles and positions is highly developed for social systems that involve only pairwise interactions among actors - however, in contemporary social network analysis it is increasingly common to use models that can take into account higher-order interactions as well. In this paper we take a category-theoretic approach to the question of how to lift role and positional analysis from graphs to hypergraphs, which can accommodate higher-order interactions. We use the framework of universal coalgebra - a 'theory of systems' with origins in computer science and logic - to formalize the main concepts of role and positional analysis and extend them to a large class of structures that includes both graphs and hypergraphs. As evidence for the validity of our definitions, we prove a very general functoriality theorem that specializes, in the case of graphs, to a folkloric observation about the compatibility of positional and role analysis. |
| title | Coalgebraic analysis of social systems |
| topic | Social and Information Networks Discrete Mathematics Symbolic Computation Category Theory |
| url | https://arxiv.org/abs/2602.23211 |