I have a problem with the RandomWalkBetweenness-Algorithm. The Graphs I want to analyse are very often transformed into so called
singular-matrices. The problem is that Colt can not work with this kind of matrices. Is there a way to chack the Graph on this "singularity" before calling the algorithm ? And what does it mean "singularity" in a graph.
Thank you for your help
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(I think that this has been answered elsewhere, but just for completeness...)
My best guess offhand is that a matrix is usually going to be called singular if the graph decomposes into > 1 component (maybe > 1 strongly connected component if the graph is directed). However, there are singular matrices whose corresponding graphs have 0 or 1 components (see http://mathworld.wolfram.com/SingularMatrix.html for some trivial examples; the last one in their 2x2 list corresponds to the complete graph on 2 vertices with self-loops).
At one point I spent some time trying to work out what the inverse of a graph was (in the 'matrix inverse' sense); there may be a good intuition for it, but I didn't develop one. (Graph multiplication is fairly straightforward, but the idea of trying to figure out the graph G^-1 such that G*G^-1 yields a graph with all self-loops is just bizarre to me.) At some point I may pound on that some more just so that I can put that problem to bed...but it won't be soon. :)
Joshua
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hello,
I have a problem with the RandomWalkBetweenness-Algorithm. The Graphs I want to analyse are very often transformed into so called
singular-matrices. The problem is that Colt can not work with this kind of matrices. Is there a way to chack the Graph on this "singularity" before calling the algorithm ? And what does it mean "singularity" in a graph.
Thank you for your help
Co_ask!
Thanks in advance!
(I think that this has been answered elsewhere, but just for completeness...)
My best guess offhand is that a matrix is usually going to be called singular if the graph decomposes into > 1 component (maybe > 1 strongly connected component if the graph is directed). However, there are singular matrices whose corresponding graphs have 0 or 1 components (see http://mathworld.wolfram.com/SingularMatrix.html for some trivial examples; the last one in their 2x2 list corresponds to the complete graph on 2 vertices with self-loops).
At one point I spent some time trying to work out what the inverse of a graph was (in the 'matrix inverse' sense); there may be a good intuition for it, but I didn't develop one. (Graph multiplication is fairly straightforward, but the idea of trying to figure out the graph G^-1 such that G*G^-1 yields a graph with all self-loops is just bizarre to me.) At some point I may pound on that some more just so that I can put that problem to bed...but it won't be soon. :)
Joshua