As　modern　parallel　computer　systems　continue　to　grow　in　scale,　the　occurrence　of　failures　becomes　inevitable,　which　places　severe　reliability　challenges　on　the　systems＇　underlying　interconnection　network.　Recently,　two　novel　indicators,　named　the　matroidal　connectivity　and　conditional　matroidal　connectivity,　were　proposed　to　better　evaluate　the　reliability　of　interconnection　networks.　These　indicators　enable　flexible　restrictions　on　faulty　edges　in　each　dimension　and　have　proven　to　be　promising　in　improving　the　edge　fault-tolerance　of　interconnection　networks.　In　this　paper,　we　aim　to　apply　these　indicators　to　the　n-dimensional　star　graph　S-n,　which　is　a　famous　interconnection　network　with　high　symmetry　and　recursive　hierarchical　structure.　We　partition　the　faulty　edge　set　F　subset　of　E(S-n)　into　i!-1　parts　according　to　each　faulty　edge＇s　dimension.　By　sorting　the　cardinality　of　these　parts　and　exerting　the　restriction　that　the　(n-i)-th　largest　part＇s　cardinality　does　not　exceed　i!-1　for　1　＜=　i　＜=　n-1,　we　prove　that　S-n-F　is　always　connected　where　|F|＜=&　sum;(n-1)(i=1)=1-1(i!-1).　Then　we　determine　the　exact　values　of　matroidal　connectivity　and　conditional　matroidal　connectivity　of　star　graphs.　Moreover,　we　make　comparisons　to　demonstrate　our　results　outperform　other　similar　works　in　terms　of　edge　fault-tolerance.