Characterizations of complete directed trees and two-trees

This paper presents necessary and sufficient conditions for a directed tree in the associated directed graph of a general network to be nonredundant. Based on these characterizations, new topological formulas for general network functions are presented that will not result in cancellations due to duplications. The relationships between the complete directed trees and two-trees and the complete trees and two-trees of the voltage and the current graphs of the Coates-Mayeda formulation are also discussed. An illustrative example is given.