- An interesting article of
Michaël Fanuel and Johan Suykens on diffusion on directed digraphs. They also look
at generalized Laplacians.
- While working on
Universality and
Barycentric numbers, found Horak, Josts article on
Spectra of combinatorial {L}aplace operators on simplicial complexes.
The discrete form Laplacians have been defined already by Poincare.
So far, it seems that
the McKean Singer paper is the first
appearance of the Dirac operator for graphs or Simplicial complexes. The
super symmetry is easy to explain there. In my McKean Singer paper,
also the first occurances of graphs with isospectral form Laplacians seem have
appeared.
- Correction June 13, 2013: page 9: while Gordon is great too, the name was Sunada.
- Correction June 15, 2013: page 11: if the path starts at an even dimensional simplex, then the path is called even, otherwise odd.
- Correction June 20, 2013: page 5: there were too many P's in the calculation D (Pf) = -PD f = -Plf = -l (Pf).