The Computing First Network (CFN) is a novel network paradigm that efficiently allocates and schedules computing force, storage resources, and network capacity across cloud, edge, and device domains. Leveraging the comprehensive network perspective offered by Software-Defined Networking (SDN) and precise assessment of distributed computing resources, this paper introduces an architecture known as Software-Defined Computing First Network (SD-CFN). This architecture forms the basis for modeling computing and network resources and designing a new representation of network topology. Ultimately, the proposed architecture and the novel network topology representation undergo comprehensive analysis and validation.