TL;DR
This paper explores a graph-based dynamical system inspired by Conway's Game of Life, introducing a heuristic for graph isomorphism testing and demonstrating that features extracted from the system are unique and satisfy metric properties for small graphs.
Contribution
It presents a novel dynamical system on graphs, a new heuristic for graph isomorphism testing, and shows the features' uniqueness and metric properties for small graphs.
Findings
Features are unique for graphs with up to ten vertices.
The induced distance satisfies the triangle inequality.
The system provides a deterministic graph feature extraction method.
Abstract
We consider a specific graph dynamical system inspired by the famous Conway's Game of Life in this work. We study the properties of the dynamical system on different graphs and introduce a new efficient heuristic for graph isomorphism testing. We use the evolution of our system to extract features from a graph in a deterministic way and observe that the extracted features are unique and the distance induced by that features satisfy triangle inequality for all connected graphs with up to ten vertices.
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Taxonomy
TopicsMachine Learning and Algorithms · Graph Theory and Algorithms · Advanced Graph Neural Networks