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Large language models (LLMs)-based personal assistants may struggle to effectively utilize long-term conversational histories.Despite advances in long-term memory systems and dense retrieval methods, these assistants still fail to capture entity relationships and handle multiple intents effectively. To tackle above limitations, we propose **Associa**, a graph-structured memory framework that mimics human cognitive processes. Associa comprises an event-centric memory graph and two collaborative components: **Intuitive Association**, which extracts evidence-rich subgraphs through Prize-Collecting Steiner Tree optimization, and **Deliberating Recall**, which iteratively refines queries for comprehensive evidence collection. Experiments show that Associa significantly outperforms existing methods in retrieval and QA (question and answering) tasks across long-term dialogue benchmarks, advancing the development of more human-like AI memory systems.