Many decays of light baryons consisting of light $u,d,s$ quarks have been measured, and these measurements will help us to understand the decay properties of light baryons. In this work, we study two-body nonleptonic weak decays of light baryon octet $(T_8)$ and baryon decuplet $(T_{10})$ by the topological diagram approach (TDA) under the SU(3) flavor symmetry for the first time. We find that (1) the TDA and the SU(3) irreducible representation approach (IRA) match consistently in $T_{10}to T^{()}_{8,10}P_8$ ($P_8$ is the light pseudoscalar meson octet); (2) almost all relevant not-yet-measured $mathcal{B}(T_{10}to T_8 P_8)$ may be predicted by using three experimental data of $mathcal{B}(Omega^-to Xi^0pi^-,Xi^-pi^0,Lambda^0K^-)$, and the upper limits of $mathcal{B}(T_{10}to T{}_{10}pi^-)$ may be obtained from the experimental upper limit of $mathcal{B}(Omega^-to Xi^{*0}pi^-)$ by both the TDA and the IRA together, nevertheless, all new predicted branching ratios are too small to br reached in current experiments; (3) $T_8to T_8 P_8$ decays are quite complex in terms of the TDA, and we find that W-exchange diagrams give large and even dominant contributions by using relevant experimental data and the isospin relations.
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