In response to the limitations of the existing complex Event Extraction （EE） methods in event classification， particularly their inability to handle the issue of a single trigger word activating multiple events of the same type， a complex EE method based on event element relation recognition and complete subgraph search was proposed to improve the effects of complex event classification. Firstly， a concise word-pair relation labeling system was designed， incorporating Span relations to identify event element boundaries and Event-Internal （EI） relations to determine whether elements belonged to the same event. Secondly， a single-stage word-pair relation recognition model was constructed， where text representations were obtained through an encoding layer， event type information was injected via an event information fusion layer， and word-pair relations were predicted using a distance-aware scoring function in the prediction layer. Finally， based on the predicted EI relations， an undirected graph was built， and a recursive complete subgraph search algorithm was designed to classify event elements， thereby enabling the complete extraction complex event of all patterns theoretically. Experimental results show that the proposed method outperforms various baselines like BERT-CRF-joint， PLMEE （Pre-trained Language Model for EE）， and CasEE （Cascade decoding for EE） in complex EE on the FewFC （Few-shot Financial Corpus） and DuEE （Dataset for Chinese EE） datasets. It can be seen that the method addresses the issue of a single trigger word activating multiple events of the same type effectively， leading to a comprehensive extraction of complex events.