Connectivity　of　a　connected　graph　G,　κ(G),　is　an　important　index　in　exploring　network　topology　which　is　the　minimal　number　of　vertices　that　need　to　be　removed　to　separate　G　into　disconnected　or　trivial.　Let　G0,G1,…,Gm−1　be　m　connected　graphs　of　the　same　order.　A　matching　composition　network　G　is　constructed　by　adding　an　arbitrary　perfect　matching　between　G0　and　G1.　For　m≥3,　a　cycle　composition　network　H　is　constructed　by　adding　an　arbitrary　perfect　matching　between　Gi　and　Gi+1(modm)　for　each　0≤i≤m−1.　This　construction　has　been　so　widely　used　in　literature　to　build　networks　in　which　fault　diagnosability　can　be　studied,　that　it　is　worth　to　study　their　connectivity　in　detail,　this　is　the　main　purpose　of　this　paper.　In　this　paper,　we　determine　(1)　κ(G)=δ(G)　if　κ(G0)+κ(G1)≥δ(G);　otherwise,　κ(G)≥κ(G0)+κ(G1),　and　(2)　κ(H)=δ(H)　if　∑i=0m−1κ(Gi)≥δ(H);　otherwise,　κ(H)≥∑i=0m−1κ(Gi).　Examples　show　those　bounds　are　tight.　We　then　generalize　these　examples　to　a　general　composition　using　matchings　on　which　we　propose　a　conjecture　on　the　connectivity　and　prove　it　for　an　important　particular　case.　©　2022