  This paper introduces the Strain Elevation Tension Spring embedding (SETSe)
algorithm, a graph embedding method that uses a physics model to create node
and edge embeddings in undirected attribute networks. Using a low-dimensional
representation, SETSe is able to differentiate between graphs that are designed
to appear identical using standard network metrics such as number of nodes,
number of edges and assortativity. The embeddings generated position the nodes
such that sub-classes, hidden during the embedding process, are linearly
separable, due to the way they connect to the rest of the network. SETSe
outperforms five other common graph embedding methods on both graph
differentiation and sub-class identification. The technique is applied to
social network data, showing its advantages over assortativity as well as
SETSe's ability to quantify network structure and predict node type. The
algorithm has a convergence complexity of around $\mathcal{O}(n^2)$, and the
iteration 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.
