Symmetry Detection and Classification in Drawings of Graphs

  • Felice De Luca
  • Md. Iqbal HossainEmail author
  • Stephen Kobourov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)


Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and especially reflectional symmetries, are also important in drawings of graphs. Detecting and classifying symmetries can be very useful in algorithms that aim to create symmetric graph drawings and in this paper we present a machine learning approach for these tasks. Specifically, we show that deep neural networks can be used to detect reflectional symmetries with 92% accuracy. We also build a multi-class classifier to distinguish between reflectional horizontal, reflectional vertical, rotational, and translational symmetries. Finally, we make available a collection of images of graph drawings with specific symmetric features that can be used in machine learning systems for training, testing and validation purposes. Our datasets, best trained ML models, source code are available online.



This work is supported in part by NSF grants CCF-1740858, CCF-1712119, DMS-1839274, and DMS-1839307. This experiment uses High Performance Computing resources supported by the University of Arizona TRIF, UITS, and RDI and maintained by the University of Arizona Research Technologies department.


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Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of ArizonaTucsonUSA

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