Hello everyone, I am solving a graph partitioning problem. I found an unnormalized Laplacian matrix of a graph, then since I have 4 processes and I am using spectral partitioning algorithm, I calculated 4 eigenvectors corresponding to 4 smallest eigenvalues of this Laplacian matrix.
Then, since I am using the k-means clustering algorithm, I formed a matrix U whose columns are these eigenvectors. After that, I clustered each row of U according to the k-means algorithm. Now, I have different row vectors at different processes, as I want. In other words, my eigenvectors have 72 elements. So, right now, I have 72 different row vectors with 4 elements. Those 72 row vectors were clustered but not in a serial order. For instance, the 4th vector is in the first process and the 5th one is in the 4th process. As the last part of my work, I want to find mincut of this partitioning but I couldn't understand how to do it. If I didn't use k-means algorithm, I would use MatPartitioningApply but now, since I clustered row vectors of U according to the index set I obtained from k-means algorithm, I don't know how to use partitioning routines. Should I form another matrix by reordering these vectors and then partition? But then, how can I be sure the vectors stay in the same process as before? Besides MatPartitioning routines, is there any routine I can use for this? I thought MatColoring can work but I guess it won't. Thanks a lot! Eda
