Most previous studies of functional brain networks have been conducted on undirected networks despite the fact that direction of information flow is able to provide additional information on how one brain region influences another. The current study explores the application of normalized transfer entropy (NTE) to detect and identify the patterns of information flow in the functional brain networks derived from EEG data during cognitive activity. Using a combination of signal processing, information and graph-theoretic techniques, this study has identified and characterized the changing connectivity patterns of the directed functional brain networks during different cognitive tasks. The functional brain networks constructed from EEG data using non-linear measure NTE also exhibit small-world property. An exponential truncated power-law fits the in-degree and out-degree distribution of directed functional brain networks. The empirical results demonstrate not only the application of transfer entropy in evaluating the directed functional brain networks, but also in determining the information flow patterns and thus provide more insights into the dynamics of the neuronal clusters underpinning cognitive function.