  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 $\mathcal{B}(\Omega^-\to \Xi^0\pi^-,\Xi^-\pi^0,\Lambda^0K^-)$, 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) $T_8\to T'_8
P_8$ 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.
