Abstract
This paper proposes three models of adding relations to an organization structure which is a complete K-ary tree of height H: (i) a model of adding an edge between two nodes with the same depth N, (ii) a model of adding edges between every pair of nodes with the same depth N and (iii) a model of adding edges between every pair of siblings with the same depth N. For each of the three 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.
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