165
Thus, by contradiction, the assumption is not true. In other words, there does
not exist a minimum RatioCut which separates at least a pair of nodes x V 1 and x V 2
into different groups in a RatioCut of two clusters. Similarly, the RatioCut consistency of more than two clusters can be proved, since the Cut variables caused by the
unrelated clusters are constant.
Therefore, the RatioCut clustering results would not separate the two versions
of any node x V 1 and x V 2 into two different groups by using our approach.
Thus, by contradiction, the assumption is not true. In other words, there does
not exist a minimum RatioCut which separates at least a pair of nodes x V 1 and x V 2
into different groups in a RatioCut of two clusters. Similarly, the RatioCut consistency of more than two clusters can be proved, since the Cut variables caused by the
unrelated clusters are constant.
Therefore, the RatioCut clustering results would not separate the two versions
of any node x V 1 and x V 2 into two different groups by using our approach.