Connectivity　is　a　classic　measure　for　reliability　of　a　multiprocessor　system　in　the　case　of　processor　failures.　Extra　connectivity　and　component　connectivity　are　two　important　indicators　of　the　reliability　of　a　multiprocessor　system　in　presence　of　failing　processors.　The　h-extra　connectivity　κh(G)　of　a　graph　G　is　the　minimum　number　of　nodes　whose　removal　will　disconnect　G,　and　every　remaining　component　has　at　least　h+1　nodes.　Moreover,　the　h-component　connectivity　cκh(G)　of　G　is　the　minimum　number　of　nodes　whose　deletion　results　in　a　graph　with　at　least　h　components.　However,　the　extra　connectivity　and　component　connectivity　of　many　well-known　networks　have　been　independently　investigated.　In　this　paper,　we　determine　the　relationship　between　extra　connectivity　and　component　connectivity　of　general　networks.　As　applications,　the　extra　connectivity　and　component　connectivity　are　explored　for　some　well-known　networks,　including　complete　cubic　networks,　hierarchical　cubic　networks,　generalized　exchanged　hypercubes,　dual-cube-like　networks,　Cayley　graphs　generated　by　transposition　trees　and　hierarchical　hypercubes　as　well.　©　2020　The　British　Computer　Society.　All　rights　reserved.