Graph theory is a branch of discrete mathematics that deals with the connections among entities. It has been proven to be a very beneficial and powerful mathematical tool and has a wide range of applications to handle complex problems in various domains. The aim of this work is two folds: first, to understand the basic notion of graph theory and second, to emphasis the significance of graph theory through a real-time application used as a representational form and characterization of brain connectivity network, as is machine learning for classifying groups depending on the features extracted from images. This application uses different techniques including preprocessing, correlations, features or algorithms. This paper illustrates an automatic tool to perform a standard process using images of the Magnetic Resonance Imaging (MRI) machine. The process includes preprocessing, building the graph per subject with different correlations, atlas, relevant feature extraction according to the literature, and finally providing a set of machine learning algorithms that can produce analyzable results for physicians or specialists. Further, to demonstrate the importance of graph theory, this article addresses the most common applications for graph theory in various fields.