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Contact tracing is a well-established and effective approach for the containment of the spread of infectious diseases. While Bluetooth-based contact tracing method using phones has become popular recently, these approaches suffer from the need for a critical mass adoption to be effective. In this paper, we present WiFiTrace, a network-centric approach for contact tracing that relies on passive WiFi sensing with no client-side involvement. Our approach exploits WiFi network logs gathered by enterprise networks for performance and security monitoring, and utilizes them for reconstructing device trajectories for contact tracing. Our approach is specifically designed to enhance the efficacy of traditional methods, rather than to supplant them with new technology. We designed an efficient graph algorithm to scale our approach to large networks with tens of thousands of users. The graph-based approach outperforms an indexed PostgresSQL in memory by at least 4.5X without any index update overheads or blocking. We have implemented a full prototype of our system and deployed it on two large university campuses. We validated our approach and demonstrate its efficacy using case studies and detailed experiments using real-world WiFi datasets.