The topography of the electrical field does not vary randomly with time but rather displays short periods of stable topographical configurations or spatial patterns, known as microstates. The search of such patterns takes place in the high dimensional electrode space with all the problems that comes with it. In this paper, we present a technique for the extraction, detection and representation of EEG microstates based on the Local Global graph(LG graph). We use the Local Global graph to represent the spatial configuration of the topographic map and use a LG graph matching approach to determine the different microstates. The proposed method was applied on the average, over trials, Event related potential recording presenting a positive peak known as P300. Five dominant microstates were identified using our methodology. During the whole period of the P300 peak there is one active microstate which presents frontal and parietal topography which is expected for the phase locked activations of the P300. The LG graph modeling of the EEG topography provides a flexible descriptor for the EEG topography and can be used for the efficient microstate segmentation of the EEG.