A model of placing a liaison in the same level of a pyramid organization structure

This paper proposes a model of placing a liaison which forms relations to all members with the same level in a pyramid organization structure such that the communication of information between every member in the organization becomes the most efficient. For the model of adding a node of liaison which gets adjacent to all nodes with the same depth N in a complete K-ary tree of height H which can describe the basic type of a pyramid organization, we obtained an optimal depth N* which maximizes the sum of shortening lengths of shortest paths between every pair of all nodes in a complete K-ary tree. It is shown that the optimal depth is N* = H, irrespective of K. This result means that the most efficient level of forming relations to a liaison is the lowest level of the organization structure, irrespective of the number of subordinates.