Fault　detection　and　localization　are　vital　for　ensuring　the　stability　of　data　center　networks　(DCNs).　Specifically,　adaptive　fault　diagnosis　is　deemed　a　fundamental　technology　in　achieving　the　fault　tolerance　of　systems.　The　highly　scalable　data　center　network　(HSDC)　is　a　promising　structure　of　server-centric　DCNs,　as　it　exhibits　the　capacity　for　incremental　scalability,　coupled　with　the　assurance　of　low　cost　and　energy　consumption,　low　diameter,　and　high　bisection　width.　In　this　paper,　we　first　determine　that　both　the　connectivity　and　diagnosability　of　the　m-dimensional　complete　HSDC,　denoted　by　(Formula　presented.),　are　m.　Further,　we　propose　an　efficient　adaptive　fault　diagnosis　algorithm　to　diagnose　an　(Formula　presented.)　within　three　test　rounds,　and　at　most　(Formula　presented.)　tests　with　(Formula　presented.)　(resp.　at　most　nine　tests　with　(Formula　presented.)),　where　(Formula　presented.)　is　the　total　number　of　nodes　in　(Formula　presented.).　Our　experimental　outcomes　demonstrate　that　this　diagnosis　scheme　of　HSDC　can　achieve　complete　diagnosis　and　significantly　reduce　the　number　of　required　tests.　©　2024　by　the　authors.