Electrophysiological Source Imaging (ESI) refers to reconstructing the underlying brain source activation from non-invasive Electroencephalography (EEG) and Magnetoencephalography (MEG) measurements on the scalp. Estimating the source locations and their extents is a fundamental tool in clinical and neuroscience applications. However, the estimation is challenging because of the ill-posedness and high coherence in the leadfield matrix as well as the noise in the EEG/MEG data. In this work, we proposed a combinatorial search framework to address the ESI problem with a provable optimality guarantee. Specifically, by exploiting the graph neighborhood information in the brain source space, we converted the ESI problem into a graph search problem and designed a combinatorial search algorithm under the framework of A* to solve it. The proposed algorithm is guaranteed to give an optimal solution to the ESI problem. Experimental results on both synthetic data and real epilepsy EEG data demonstrated that the proposed algorithm could faithfully reconstruct the source activation in the brain.