A Method of Tree Expansion in Network Topology

This paper presents a systematic method of obtaining the total sum of all possible tree admittance products of a very complicated network. First, such a network is partitioned into several simple subnetworks by a set of independent cut sets. Then, the relationship between trees or tree admittance products of the network and multitrees or multitree admittance products of each subnetwork is found and presented as the tree expansion theorem. Finally, an effective method for decomposition of the large network into simple subnetworks is discussed. The methods described in this paper are very suitable for use by automatic computation.