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cluster-analysismetis

Interpretation of 'ufactor' on a toy graph clustering

I am trying to do a imbalanced partition by METIS. I do not need equal number of vertices in each cluster(which is done by default in METIS). My graph has no constraints, it's a undirected unweighted graph. Here is a example toy graph clustered by METIS without no ufactor parameter.

enter image description here

Then, i tried with different ufactor and at value 143, METIS starts to do the expected cluster like the following-

enter image description here

Can anybody interpret this. Eventually, I want to find a way to guess an ufactor from any unbalanced and undirected graph that will minimize the normalized cut without doing any balance necessarily.

Solution

  • Imbalance=1+(ufactor/1000). By default imbalance=1. Number of vertex in largest cluster-

     imbalance*(number of vertex/number of cluster)

    For first picture(default clustering)- number of vertex in larges cluster- 1*(14/2)=7, so the second cluster is also 14-7=7 In the second picture(ufactor 143)-

    imbalance=1+143/1000=1.143

so, 1.143*(14/2)=8.001

    That allows the largest cluster to have 8 vertex.