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Existing neural models for dialogue response generation assume that utterances are sequentially organized. However, many real-world dialogues involve multiple interlocutors (i.e., multi-party dialogues), where the assumption does not hold as utterances from different interlocutors can occur ``in parallel.'' This paper generalizes existing sequence-based models to a Graph-Structured neural Network (GSN) for dialogue modeling. The core of GSN is a graph-based encoder that can model the information flow along the graph-structured dialogues (two-party sequential dialogues are a special case). Experimental results show that GSN significantly outperforms existing sequence-based models.