Wireless　Body　Area　Networks　(WBANs)　have　received　considerable　attention　in　recent　years.　Several　sensors　are　placed　in　and　around　the　human　body　to　gather　health　information.　One　of　the　main　challenges　in　WBANs　is　the　design　of　a　Medium　Access　Control　(MAC)　protocol　that　plays　a　vital　role　for　the　efficient　functionality.　In　this　paper　we　propose　a　graph-based　priority-aware　MAC　protocol　for　WBANs.　The　network　cluster-tree　topology　is　modeled　as　an　interference　graph.　Using　graph　coloring　scheme,　the　contention-free　time　slots　are　assigned　to　the　sensor　nodes.　Data　priority　is　considered　in　the　procedure　of　time　slot　reallocation.　Simulation　results　show　that　the　scheme　improves　the　network　performance.　©　2019　IEEE.