Deep　learning　based　human　brain　network　classification　has　gained　increasing　attention　in　recent　years.　However,　current　methods　remain　limited　in　exploring　the　topological　structure　information　of　a　brain　network.　In　this　paper,　we　propose　a　kind　of　new　convolutional　kernels　with　an　element-wise　weighting　mechanism　(CKEW)　to　extract　hierarchical　topological　features　of　brain　networks,　in　which　each　weight　is　assigned　to　an　element　with　a　unique　neuroscientific　meaning.　In　addition,　a　novel　classification　framework　based　on　CKEW　is　presented　to　diagnose　brain　diseases　and　explore　the　most　important　original　features　by　a　tracing　feature　analysis　method　efficiently.　Experimental　results　on　two　autism　spectrum　disorder　(ASD)　datasets　and　an　attention　deficit　hyperactivity　disorder　(ADHD)　dataset　with　functional　magnetic　resonance　imaging　(fMRI)　data　demonstrate　that　our　method　can　more　accurately　distinguish　subject　groups　compared　to　several　state-of-the-art　methods　in　cerebral　disease　classification,　and　abnormal　connectivity　patterns　and　brain　regions　identified　are　more　likely　to　become　biomarkers　associated　with　a　cerebral　disease.　(C)　2020　Elsevier　Ltd.　All　rights　reserved.