Guiding Network Analysis using Graph Slepians: An Illustration for the C. Elegans Connectome

Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then transpose signal processing operations to graphs by implementing them in the spectral domain. Here, we build on recent work that generalized Slepian functions to the graph setting. In particular, graph Slepians are band-limited graph signals with maximal energy concentration in a given subgraph. We show how this approach can be used to guide network analysis; i.e., we propose a visualization that reveals network organization of a subgraph, but while striking a balance with global network structure. These developments are illustrated for the structural connectome of the C. Elegans.