Connectivity　indicators　are　commonly　used　to　evaluate　system　fault　tolerance　and　reliability.　However,　with　the　high　demand　for　multi-processor　systems　in　high-performance　computing　and　data　center　networks,　the　number　of　processors　is　getting　larger,　and　the　network　is　getting　more　complex.　Thus,　traditional　connectivity　and　other　indicators　are　hardly　competent　in　assessing　the　reliability　of　complex　networks.　The　matroidal　connectivity　and　conditional　matroidal　connectivity　are　novel　connectivity　metrics　that　measure　the　actual　fault-tolerant　capability　based　on　the　constraints　of　each　network　dimension.　In　this　paper,　we　study　matroidal　connectivity　and　conditional　matroidal　connectivity　of　the　(n,k)-arrangement　graph　network　An,k　from　the　natural　perspective　of　the　partition　of　edge　dimension　and　obtain　their　theoretically　accurate　values.　Moreover,　we　conduct　numerical　analysis　to　compare　matroidal　connectivity　with　other　conditional　edge　connectivities　in　An,k.　Additionally,　we　explore　the　distribution　pattern　of　edge　failure　through　simulation　experiments　in　An,k　and　attain　the　relation　of　conditional　matroidal　connectivity　related　to　network　scales.　Our　investigations　include　two　famous　network　classes:　alternating　group　graphs　and　star　graphs.　©　2024　Elsevier　B.V.