Appendix F
Example MATLAB
functions to implement
spectral embeddings
This appendix provides MATLAB library functions that implement the basic spectral embeddings that we have discussed. They each return the appropriate eigenvector matrices that provide the coordinates for embedding each network.
The included functions are:
• Laplacian — implements three of the standard Laplacian embeddings for an
undirected network.
• DirLaplacian — implements our directed spectral embedding.
• DirLaplacianChung — implements the directed spectral embedding designed
by Fan Chung.
• SignedLaplacian — implements our signed spectral embedding given two positive matrices, representing the strength of positive and negative relationships.
• TypedDirLaplacian — implements our composition of typed and directed edges;
calls DirLaplacian.
• TemporalDirLaplacian — implements our composition of directed edges with
temporal changes in intensity; calls TypedDirLaplacian.
• TypedLaplacian — implements spectral embedding of a typed network using
Chung’s directed embedding; calls DirLaplacianChung.
• TemporalLaplacian — implements spectral embedding of networks with temporal changes in intensity; calls DirLaplacianChung.
• SignedDirLaplacian — implements our composition of signed and directed
networks.
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