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Visualization has proven to be a useful tool for understanding network structures. Yet the dynamic nature of social media networks requires powerful visualization techniques that go beyond static network diagrams. To provide strong temporal network visualization tools, designers need to understand what tasks the users have to accomplish. This paper describes a taxonomy of temporal network visualization tasks. We identify the 1) entities, 2) properties, and 3) temporal features, which were extracted by surveying 53 existing temporal network visualization systems. By building and examining the task taxonomy, we report which tasks are well covered by existing systems and make suggestions for designing future visualization tools. The feedback from 12 network analysts helped refine the taxonomy.