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In neurophysiology, it is important to quantify the causal neural interactions and infer the underlying complex networks from neurophysiological recordings such as electroen-cephalogram (EEG). Existing methods such as Granger causality are model dependent and thus cannot quantify nonlinear dependencies. In this paper, directed information (DI) is used to quantify the causality of the interactions and time-lagged directed information is proposed to simplify the computation of DI. To distinguish the direct from indirect connections in network inference, conditional directed information (CDI) is introduced. Based on DI and CDI, a network inference algorithm is proposed to infer the functional networks underlying EEG activity. The proposed algorithm is applied to both simulated data and EEG data to evaluate its effectiveness.