The Signatures of Ideal Flow Networks

An Ideal Flow Network (IFN) is a strongly connected network where relative flows are preserved (irreducible premagic matrix). IFN can be decomposed into canonical cycles to form a string code called network signature. A network signature can be composed back into an IFN by assignment and merging operations. Using string manipulations on network signatures, we can derive total flow, link values, sum of rows and columns, and probability matrices and test for irreducibility.