Separate brain regions exhibit synchronous intrinsic activity used to assess connectivity patterns known to appear among brain areas. Connectivity is evaluated from functional magnetic resonance imaging (fMRI) measuring the blood oxygen level dependent signal (BOLD) signal. Extensive research has revealed a distinctive pattern of connectivity among brain areas that can be visualized through a functional connectivity matrix (FCM) matrix. As in any measurement, BOLD signals are subject to contamination from noise and nuisances unrelated to brain's intrinsic activity. Up until now, little work has been developed to determine if patterns observed in FCMs occurred by chance or were driven by a more deterministic process. This work proposes a mathematical framework to test the randomness of FCM connectivity patterns in a systematic and statistical way. A cohort of 121 healthy controls is used to demonstrate the usefulness of the proposed framework. Results indicate that particular parts of the brain might exhibit decreasing randomness with age and gender. Results also show the framework's effectiveness in assessing FCM randomness.