Title: When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum,
Abstract: The study of complex systems benefits from graph models and their analysis.
In particular, the eigendecomposition of the graph Laplacian lets emerge
properties of global organization from local interactions; e.g., the Fiedler
vector has the smallest non-zero eigenvalue and plays a key role for graph
clustering. Graph signal processing focusses on the analysis of signals that
are attributed to the graph nodes. The eigendecomposition of the graph
Laplacian allows to define the graph Fourier transform and extend conventional
signal-processing operations to graphs. Here, we introduce the design of
Slepian graph signals, by maximizing energy concentration in a predefined
subgraph for a graph spectral bandlimit. We establish a novel link with
classical Laplacian embedding and graph clustering, which provides a meaning to
localized graph frequencies.