Event causality identification (ECI) focuses on detecting causal relationships between events within a document. Existing approaches typically treat each event-mention pair independently, overlooking the relational dynamics and potential conflicts among event causalities. To tackle this challenge, we propose the Event-induced Graph with Constraints (EiGC), which models the complex event-level causal structures in a more realistic manner, facilitating comprehensive causal relation identification. To be more specific, we construct a graph based on diverse event-driven knowledge sources, such as coreference and co-occurrence relations. A graph convolutional network (GCN) is then employed to encode these structural features, effectively capturing both local and global dependencies between nodes. Additionally, we implement event-aware constraints through integer linear programming, incorporating the principles of uniqueness, non-reflexivity, and coreference consistency in event-causal relationships. This approach ensures logical consistency and prevents conflicts in the prediction outcomes. Experimental results on three widely used datasets illustrate that our proposed EiGC approach achieves excellent performance among all the baseline models.