# When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

arXiv: https://arxiv.org/abs/1701.08401 · HTML: https://mlsanity.com/paper/1701.08401/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2017.

## Built on by (most cited first, 2 of 2)

- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [SlepNet: Spectral Subgraph Representation Learning for Neural Dynamics](https://mlsanity.com/paper/2506.16602/) (2025)

## Abstract (arXiv)

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.