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This paper proposes two models of adding relations to a linking pin type organization structure where every pair of siblings in a complete K-ary tree of height H is adjacent: (i) a model of adding an edge between two nodes with the same depth N and (ii) a model of adding edges between every pair of nodes with the same depth N. For each of the two models, an optimal depth N* is obtained by maximizing the total shortening path length which is the sum of shortening lengths of shortest paths between every pair of all nodes. [ABSTRACT FROM AUTHOR]