As　a　novel　non-neural　network　style　deep　learning　method,　the　deep　forest　can　perform　effective　feature　learning　without　relying　on　a　large　amount　of　training　data,　thus　brings　us　some　opportunities　to　accurately　classify　brain　networks　(BNs)　on　limited　fMRI　data.　Currently,　preliminary　attempts　to　use　deep　forest　to　classify　BNs　are　already　emerging.　However,　these　studies　simply　adopted　the　sliding　windows　to　scan　the　inputted　BNs　and　failed　to　consider　the　inherent　sparsity　of　BNs,　which　makes　them　susceptible　to　those　redundant　edges　in　BNs　with　little　weight.　In　this　paper,　we　propose　a　deep　forest　framework　with　sparse　topological　feature　extraction　and　hash　mapping　(DF-STFEHM)　for　BN　classification.　Specifically,　we　first　design　an　extremely　random　forest　guided　by　a　weighted　random　walk　(ERF-WRW)　to　extract　sparse　topological　features　from　BNs,　where　the　random　walk　strategy　is　used　to　capture　their　topological　structures　and　the　weighted　strategy　is　used　to　reduce　the　influence　of　redundant　edges　with　little　weight.　Then,　we　map　these　sparse　topological　features　into　a　compact　hashing　space　by　a　kernel　hashing,　which　can　better　preserve　topological　similarities　of　brain　networks　in　the　hashing　space.　Finally,　the　obtained　hash　codes　are　fed　into　the　casForest　to　perform　deeper　feature　learning　and　classification.　Experimental　results　on　ABIDE　I　and　ADHD-200　datasets　show　that　the　DF-STFEHM　outperforms　several　state-of-the-art　methods　on　classification　performance　and　accurately　identifies　abnormal　brain　regions.