Solving Higher-Order Graphs Method: A Linear Analytical Treatment

Abstract

Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can be enumerated and represented by ordinals. The method allows one to extract partial information and gives an alternative to classical graph approach. An analysis of higher-order graphs as potent tool to generate algorithms for SoS, IoT, quantum communications, neuronal networks models, multiple interferometric devices is also reported.