  We study junctions of supersymmetric domain walls in N=1 supergravity
theories in four dimensions, coupled to a chiral superfield with quartic
superpotential having $Z_3$ symmetry. After deriving a BPS equation of the
domain wall junction, we consider a stable hexagonal configuration of network
of brane junctions, which are only approximately locally BPS. We propose a
model for a mechanism of supersymmetry breaking without loss of stability,
where a messenger for the SUSY breaking comes from the neighboring anti-BPS
junction world, propagating along the domain walls connection them.
