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KNN Graphs & Interconnectivity

  • k-nearest graphs from an original data in 2D:
  • EC{Ci ,Cj } :The absolute inter-connectivity between Ci and Cj: the sum of the weight of the edges that connect vertices in Ci to vertices in Cj
  • Internal inter-connectivity of a cluster Ci : the size of its min-cut bisector ECCi (i.e., the weighted sum of edges that partition the graph into two roughly equal parts)
  • Relative Inter-connectivity (RI): 

\[RI(C_{i},C_{j})=\frac{|EC_{C_{i},C_{j}}|}{\frac{|EC_{C_{i}}|+|EC_{C_{j}}|}{2}}\]



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