Functional connectivity of cognitive tasks allows researchers to analyse the interaction mapping occurring between different regions of the brain using electroencephalography (EEG) signals. Standard practice in functional connectivity involve studying the electrode pair interactions across several trials. As the cognitive task always involves the human factor, it is inevitable to have lower quality data from the brain signals influenced by the subject concentration or other mental states which can occur anytime over the whole experimental trials. The connectivity among electrodes are heavily influenced by these low quality EEG. In this paper, we aim at enhancing the functional connectivity of mental tasks by implementing a classification step in the process to remove those incorrect EEG trials from the available set. The classification step removes the trials which were mis-classified or had a low probability of occurrence to extract only reliable EEG trials. Through our approach, we have successfully improved the separability among graph parameters for different mental tasks. We also observe an improvement in the readability of the connectivity by focusing only on a group of selected channels rather than employing all the channels.