The network of a structure can be described as a connected directed or undirected graph G_H=(V_H,E_H) where the set of connected nodes are V_H and the set of direct link between the nodes are E_H . An inter connection network provides the physical connection between different components by parallel or circular system. Inter connection networks of many graph have been studied for the reliability and efficiency. In this paper a Honey comb Network is obtained by interconnecting perfectly matched circular graph at each stage of its growth. Also the size of the Honey comb Network at the nth –stage of its growth is obtained by interconnecting nodes. Perfectly matched graph is based on geometric multiplicity.

Graph Theory, Matching, Maximum Matching, Geometric Multiplicity, sparse graph, Honey Comb Network, Hexagon..