This paper presents a brain based biometrics methodology using local global (L-G) and stochastic Petri net (SPN) graphs. In particular, today?s most used lying detection systems (polygraph) are based on blood pressure under certain psychological conditions and have been proven inadequate and inaccurate for determining if a person is saying the truth or not. The main reason behind this inaccuracy is the psychological conditions under the test is contacting. Innocent persons with psychological fear to police or FBI agents may inappropriately react during the test producing false alarms, while at the same time guilty persons with acting capabilities may be lying and pass the test. Here in this paper we present a methodology based on fMRI and the way that the brain cells or brain regions interact regarding thinking and/or executing certain tasks. More specifically, fMRI provides color images for the active regions of the brain during thinking and/or performing certain tasks. These region-images are extracted and geometrically (topologically) are associated with the L-G graphs. Then using SPN graphs we represent their functionality. Thus, comparing the L-G and SPN graphs extracted from the candidate fMRI images to a set of "correct" generic L-G and SPN graph models available in an L-G/SPN graph Database offers a more accurate measurement of the truth of false answers during the test. The main reason about the accuracy is that a liar will be detected because he/she will try to "think" how to avoid the truth.