Current methods for event representation ignore related events in a corpus-level global context. For a deep and comprehensive understanding of complex events, we introduce a new task, Event Network Embedding, which aims to represent events by capturing the connections among events. We propose a novel framework, Global Event Network Embedding (GENE), that encodes the event network with a multi-view graph encoder while preserving the graph topology and node semantics. The graph encoder is trained by minimizing both structural and semantic losses. We develop a new series of structured probing tasks, and show that our approach effectively outperforms baseline models on node typing, argument role classification, and event coreference resolution.