Abstract
This work explores the definiteness of the weighted graph Laplacian matrix with negative edge weights. The definiteness of the weighted Laplacian is studied in terms of certain matrices that are related via congruent and similarity transformations. For a graph with a single negative weight edge, we show that the weighted Laplacian becomes indefinite if the magnitude of the negative weight is less than the inverse of the effective resistance between the two incident nodes. This result is extended to multiple negative weight edges. The utility of these results are demonstrated in a weighted consensus network where appropriately placed negative weight edges can induce a clustering behavior for the protocol.
| Original language | English |
|---|---|
| Article number | 7039834 |
| Pages (from-to) | 2895-2900 |
| Number of pages | 6 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 2015-February |
| Issue number | February |
| DOIs | |
| State | Published - 2014 |
| Event | 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: 15 Dec 2014 → 17 Dec 2014 |
ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
Fingerprint
Dive into the research topics of 'On the definiteness of the weighted Laplacian and its connection to effective resistance'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver