In this paper we introduce: 1) a new Artificial Neural Network (ANN) architecture, the Auto Contractive Map (AutoCM), 2) a new index to measure the complexity of a–directed graphs (the H index); 3) and a new method to translate the results of data mining into a graph representation (the Maximally Regular Graph). In particular, AutoCMs squashes the non linear correlation among variables into an embedding space where a visually transparent and cognitively natural notion such as ‘closeness’ among variables reflects accurately their associations. Through suitable optimization techniques that will be introduced and discussed in detail in what follows, ‘closeness’ can be converted into a compelling graph–theoretic representation that picks all and only the relevant correlations and organizes them into a coherent picture.Massimo Buscema (1955). Professor and Computer Scientist, expert in Neural Networks and Adaptive Artificial Systems. Director of Semeion Research Centre of Science and Communication (a Scientific Organization Recognized by Italian Ministry of Research in 1991). Professor and Director of the Department of Science of Communications at Charleston University (West Virginia-USA 1981-1985), Professor of “Computers and Linguistics” at Perugia University (1984–1985). Author of scientific publications on theoretical aspects of Natural Computation, with 18 books, and over 150 scientific articles. Inventor of 14 international patents and author of more than 30 software packages in Artificial Neural Networks and Evolutionary Systems. Riccardo Petritoli (1970): Researcher of Semeion Research Centre, electronic engineer, has developed software in medical field, implementing models of Artificial Neural Networks. He is specialized in biomedical imaging analysis techniques. Author of several scientific papers.Giovanni Pieri (1938): Associate Researcher of Semeion Research Centre, chemical engineer, he is consultant for technologic transfer in various companies and public agencies. He has been director of G. Donegani Research Center (Montedison/ENI). Published many scientific papers on chemical equipments physics.Pierluigi Sacco (1964): Professor of Economy Politics at IUAV University of Venice and Member of Scientific and Technological Committee of Semeion Research Centre. Writes for “Il Sole24Ore”. Has published several articles and scientific papers in economic theory field, on games theory and economy of the culture.