Recently,　the　growth　of　deep　learning　has　produced　a　large　number　of　deep　neural　networks.　How　to　describe　these　networks　unifiedly　is　becoming　an　important　issue.　To　make　difference　from　capsule　networks,　we　first　formalize　neuronal　(plain)　networks　in　a　mathematical　definition,　give　their　representational　graphs,　and　prove　a　generation　theorem　about　the　induced　networks　of　the　graphs.　Then,　we　extend　plain　networks　to　capsule　networks,　and　set　up　a　capsule-unified　framework　for　deep　learning,　including　a　mathematical　definition　of　capsules,　an　induced　model　for　capsule　networks　and　a　universal　backpropagation　algorithm　for　training　them.　Moreover,　we　present　a　set　of　standard　graphical　symbols　of　capsules,　neurons,　and　connections　for　application　of　the　framework　to　graphical　programming.　Finally,　we　design　and　implement　a　demo　platform　to　show　the　graphical　programming　practicability　of　deep　neural　networks　in　mouse-click　drawing　experiments.　©　2020,　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.