[petsc-dev] proposed minor PetscPartitioner changes

[Jed Brown]

Vaclav Hapla <vaclav.hapla at erdw.ethz.ch> writes:

>>> Yes. Mat can represent any graph in several different ways -
>>> e.g. Laplacian, adjacency, incidence, oriented incidence matrix. The
>>> graph could be also represented in other way like a list of vertices
>>> and edges. 
>> 
>> Also known as COO format for a matrix.
>
> You could represent by COO any of the matrices above. I don't understand how it relates to listing vertices and edges of a graph.

COO is literally a list of edges.  Square matrices and graphs are the
same thing.

>> 
>>> MatPartitioning picks just one representation as an input - the
>>> adjacency matrix. But I mean the picked representation does not
>>> matter, and the result is not a partitioning of any matrix, but
>>> partitioning of the graph. The graph is the underlying concept. This
>>> is why I don't consider the Mat prefix optimal.
>> 
>> Matrix and graph are equivalent concepts.  
>
> I think that's an overly strong statement. It sounds like a matrix and a graph are bijectively interchangeable things which is certainly not true:
> 1) As I mentioned, there are multiple ways of representing a graph by a matrix, and for a given graphs these matrix representations don't even have the same dimensions.
> 2) Even if you stick to the adjacency matrix (which you apparently do), it's still not bijective with the graph - the adjacency matrix is a square symmetric Boolean matrix. You can just say that the _sparse pattern_ of the _symmetric_ matrix is bijective with the respective graph. This is a by far weaker statement.

Graphs can have edge weights.  A symmetric matrix is an undirected
graph.  A nonsymmetric matrix is a directed graph.

> Why you then have a special matrix type MATMPIADJ which is value-less 

MatCreateMPIAdj literally has an argument named "values".

> and automatically symmetric if all matrices "are" graphs?

It is not "automatically symmetric" -- you have to declare that with
MatSetOption as documented in the man page.  A partitioner for an
undirected graph may require that the input is symmetric, much like how
CG will fail if the input is not SPD.