—This paper proposes two models of adding relations to a linking pin type organization structure where every pair of siblings in a complete Kary 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.