very well prepared lecture. i'm close to completing my first course in graph theory and investigating spectral graph theory looks like a fascinating next step to take.
(xu-xv)^2 = xu^2 -2xuxv +xv^2 = 2(xu^2+xv^2) - (xu+xv)^2 Each vertex is incident to d edges, so: sum_over_edges|xu-xv|^2 = 2d sum_over_vertices(xv^2) - sum_over_edges(xu+xv)^2
Every time I see this lecture hall I know it's going to be a great presentation.
Amazing lecture!
very good lecture. Easy to understand even with minimal graph theory background
very well prepared lecture. i'm close to completing my first course in graph theory and investigating spectral graph theory looks like a fascinating next step to take.
Nice Lecture.
at 38.50, the relation written at the top is not visible.
Will it be possible for someone to mention it as a note.
Thanks
(xu-xv)^2 = xu^2 -2xuxv +xv^2 = 2(xu^2+xv^2) - (xu+xv)^2
Each vertex is incident to d edges, so:
sum_over_edges|xu-xv|^2 = 2d sum_over_vertices(xv^2) - sum_over_edges(xu+xv)^2
Excellent!!!
Is it true that the multiplicity of 2 as an eigenvector is equal to the number of bipartite components? Seems plausible, I guess?
Anyone knows what maxcot(G) is? There's no explanation on this...
It's maximum cut
:= 1/|E| max_S [ E(S,G-S) ]
Is that a cell phone ringing?