MRG

 MRG Maximally Regular Graph   (Semeion©) 

MST (Minimum Spanning Tree) represents in “data mining” the minimum nervous system of any data structure. Anyway to explain in a complete way the complexity of a system we need to add to the MST connections those further connections between variables that have at least two characteristics :

  • they shall be relevant from quantitative point of view;
  • they shall be able to create, from a qualitative point of view, regular cyclic microstructures, inside the global structure of the system itself.

In this way the tree graph of MST becomes an indirect graph always provided with internal cycles.

The presence of internal cycles introduces in the graph the time dimension and the graph becomes a dynamic system.

grafo-mst

MST

grafo-mrg

MRG

Reference:

[1] P.M.Buscema, Auto Contractive Maps, Semeion Technical Paper 32, Aracne Publisher 2008, Rome, ISBN 978–88–548–1714–2.

[2] P.M. Buscema, P.L. Sacco, Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG): A New Methodology for Data Mining, in V. Capecchi et al. (eds.), Applications of Mathematics in Models, Artificial Neural Networks and Arts, Chapter 11, DOI 10.1007/978-90-481-8581-8_11, Springer Science+Business Media B.V. 2010).