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17 votes
3 answers
2k views

Laplacians on graphs vs. Laplacians on Riemannian manifolds: $\lambda_2$?

A graph $G$ is connected if and only if the second-largest eigenvalue $\lambda_2$ of the Laplacian of $G$ is greater than zero. (See, e.g., the Wikipedia article on algebraic connectivity.) Is ...
Joseph O'Rourke's user avatar
4 votes
1 answer
646 views

Combinatorial geodesics

[There has been a flaw in my definition - as Sergei and Andreas pointed out. I hope I could fix it.] I want to understand how the concepts of directions, straight (or shortest) lines, and geodesics &...
Hans-Peter Stricker's user avatar