Large models have emerged as the most recent groundbreaking achievements in artificial intelligence, and particularly machine learning. However, when it comes to graphs, large models have not achieved the same level of success as in other fields, such as natural language processing and computer vision. In order to promote applying large models for graphs forward, we present a perspective paper to discuss the challenges and opportunities associated with developing large graph models. First, we discuss the desired characteristics of large graph models. Then, we present detailed discussions from three key perspectives: representation basis, graph data, and graph models. In each category, we provide a brief overview of recent advances and highlight the remaining challenges together with our visions. Finally, we discuss valuable applications of large graph models. We believe this perspective paper is able to encourage further investigations into large graph models, ultimately pushing us one step closer towards artificial general intelligence (AGI).

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