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Open AccessArticle

Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs

1
Department of Optics, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria, E-28040 Madrid, Spain
2
Department of Physics, Faculty of Science, Ain Shams University, 1156 Cairo, Egypt
3
Department of Chemical Enginering, E.T.S. de Ingenieros Industriales, Universidad Politécnica de Madrid, C/José Gutiérrez Abascal, 2, E-28006 Madrid, Spain
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(11), 288; https://doi.org/10.3390/sym9110288
Received: 13 October 2017 / Revised: 17 November 2017 / Accepted: 17 November 2017 / Published: 22 November 2017
(This article belongs to the Special Issue Graph Theory)
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 for one to extract partial information and gives an alternative to classical graph approach. View Full-Text
Keywords: flow graph; matrix algebra; linear equations; cascade graph; graph order; path ordinal; path set; path set diagram flow graph; matrix algebra; linear equations; cascade graph; graph order; path ordinal; path set; path set diagram
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Kamal, H.; Larena, A.; Bernabeu, E. Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs. Symmetry 2017, 9, 288.

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