Spectral Embedding of Graph Networks

TL;DR

This paper presents a novel unsupervised graph embedding method based on a generalized Laplacian that effectively captures local and global network structures, improving performance in various data analysis tasks.

Contribution

It introduces a spectral embedding technique using a transformed graph with edge centrality weights, enhancing network representation for analysis tasks.

Findings

Significant improvement over state-of-the-art in social network analysis

Effective in material science data analysis

Successful application to SARS-CoV-2 protein interaction data

Abstract

We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure and neighborhood proximity in a single representation. The key idea is to transform the given graph into one whose weights measure the centrality of an edge by the fraction of the number of shortest paths that pass through that edge, and employ its spectral proprieties in the representation. Testing the resulting graph network representation shows significant improvement over the sate of the art in data analysis tasks including social networks and material science. We also test our method on node classification from the human-SARS CoV-2 protein-protein interactome.