References

• M. H. Trinh, H.-S. Ahn, "Matrix-weighted graphs: Theory and Applications," LNCIS 498, Springer Cham, 2026

• Instructor's slides

Course contents

1. Matrix-weighted graphs

2. Matrix-weighted Laplacian: undirected and leader-follower topologies

3. Matrix-weighted Laplacian: directed topologies

4. Electrical analogies

5. Rigidity theory

6. Connectivity: exact algorithms

7. Connectivity: heuristic algorithms

8. Spanning trees

9. Quantitative indices

10. Matrix-weighted consensus: undirected topology

11. Matrix-weighted consensus: directed topologies

12. Signed matrix-weighted graphs and bipartite matrix-weighted consensus

13. Matrix-weighted consensus with scaling matrices

14. Networked input-output economic model

15. Bearing-only control