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

TL;DR

The paper presents SETSe, a physics-inspired graph embedding algorithm that effectively differentiates and analyzes complex networks, outperforming existing methods in sub-class identification and network structure quantification.

Contribution

Introduces the SETSe algorithm, a novel physics-based graph embedding method that enhances network differentiation and sub-class detection in attribute networks.

Findings

SETSe outperforms five common graph embedding methods.

It effectively differentiates graphs with similar standard metrics.

The algorithm is fast, scalable, and provides analytical insights.

Abstract

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.