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Micro-expression recognition (MER) is valuable because micro-expressions (MEs) can reveal genuine emotions. Most works take image sequences as input and cannot effectively explore ME information because subtle ME-related motions are easily submerged in unrelated information. Instead, the facial landmark is a low-dimensional and compact modality, which achieves lower computational cost and potentially concentrates on ME-related movement features. However, the discriminability of facial landmarks for MER is unclear. Thus, this paper explores the contribution of facial landmarks and proposes a novel framework to efficiently recognize MEs. Firstly, a geometric two-stream graph network is constructed to aggregate the low-order and high-order geometric movement information from facial landmarks to obtain discriminative ME representation. Secondly, a self-learning fashion is introduced to automatically model the dynamic relationship between nodes even long-distance nodes. Furthermore, an adaptive action unit loss is proposed to reasonably build the strong correlation between landmarks, facial action units and MEs. Notably, this work provides a novel idea with much higher efficiency to promote MER, only utilizing graph-based geometric features. The experimental results demonstrate that the proposed method achieves competitive performance with a significantly reduced computational cost. Furthermore, facial landmarks significantly contribute to MER and are worth further study for high-efficient ME analysis.