2019/07/17 by Reinhard Diestel, Diestel, Reinhard
Computer Science · Physics and Astronomy · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Graph Labeling and Dimension Problems #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.1907.07341
openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby identify and discover 'types': of behaviour, views, abilities, dispositions. The mathematical theory of tangles has its origins in the connectivity theory of graphs, which it has transformed over the past 30 years. It has recently been axiomatized in a way that makes its two deepest results applicable to a much wider range of contexts. This expository paper indicates some contexts where this difference of approach is particularly striking. But these are merely examples of such contexts: in principle, it can apply to much of the quantitative social sciences. Our aim here is twofold: to indicate just enough of the theory of tangles to show how this can work in the various different contexts, and to give plenty of different examples illustrating this.