# Symmetry Detection and Classification in Drawings of Graphs

## TL;DR

This paper introduces a machine learning approach using deep neural networks to detect and classify various symmetries in graph drawings, achieving high accuracy and providing datasets and tools for further research.

## Contribution

It presents a novel deep learning method for symmetry detection and classification in graph drawings, along with publicly available datasets and code.

## Key findings

- Deep neural networks detect reflectional symmetry with 92% accuracy.
- A multi-class classifier distinguishes between four types of symmetries.
- Public datasets and trained models are provided for research use.

## Abstract

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.