Fast cancer diagnosis represents a real necessity in applied medicine due to the importance of this disease. Thus, theoretical models can help as prediction tools. Graph theory representation is one option because it permits us to numerically describe any real system such as the protein macromolecules by transforming real properties into molecular graph topological indices. This study proposes a new classification model for proteins linked with human colon cancer by using spiral graph topological indices of protein amino acid sequences. The best quantitative structure-disease relationship model is based on eleven Shannon entropy indices. It was obtained with the Naïve Bayes method and shows excellent predictive ability (90.92%) for new proteins linked with this type of cancer. The statistical analysis confirms that this model allows diagnosing the absence of human colon cancer obtaining an area under receiver operating characteristic of 0.91. The methodology presented can be used for any type of sequential information such as any protein and nucleic acid sequence.