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This paper introduces the Strain Elevation Tension Spring embedding (SETSe)algorithm, a graph embedding method that uses a physics model to create nodeand edge embeddings in undirected attribute networks. Using a low-dimensionalrepresentation, SETSe is able to differentiate between graphs that are designedto appear identical using standard network metrics such as number of nodes,number of edges and assortativity. The embeddings generated position the nodessuch that sub-classes, hidden during the embedding process, are linearlyseparable, due to the way they connect to the rest of the network. SETSeoutperforms five other common graph embedding methods on both graphdifferentiation and sub-class identification. The technique is applied tosocial network data, showing its advantages over assortativity as well asSETSe's ability to quantify network structure and predict node type. Thealgorithm has a convergence complexity of around $\mathcal{O}(n^2)$, and theiteration speed is linear ($\mathcal{O}(n)$), as is memory complexity. Overall,SETSe is a fast, flexible framework for a variety of network and graph tasks,providing analytical insight and simple visualisation for complex systems.

The spring bounces back: Introducing the Strain Elevation Tension Spring embedding algorithm for network representation