That might not have been terribly clear -- the point is, "incidence"
of edges and vertices is a binary relation.  One needs to make a
choice to orient the matrix to make the linear algebra coincidence
work out.

On Mon, Apr 22, 2013 at 8:51 AM, Tom Boothby <tomas.boot...@gmail.com> wrote:
>> Yes it does, in a way. If you want to construct the Laplacian matrix L of the
>> graph from the incidence matrix E just by using matrix multiplication,
>> you need to pick up an orientation for each edge, i.e. assigning +1 to
>> one end, and -1 to the other. Then, bingo, you have L=E.T*E
>
> I've always seen that described as: "take a random orientation of an
> incidence matrix and multiply it by its transpose to get the
> Laplacian".

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