  We consider the slow and athermal deformations of amorphous solids and show
how the ensuing sequence of discrete plastic rearrangements can be mapped onto
a directed network. The network topology reveals a set of highly connected
regions joined by occasional one-way transitions. The highly connected regions
include hierarchically organized hysteresis cycles and sub-cycles. At small to
moderate strains this organization leads to near-perfect return point memory.
The transitions in the network can be traced back to localized particle
rearrangements (soft-spots) that interact via Eshelby-type deformation fields.
By linking topology to dynamics, the network representations provides new
insights into the mechanisms that lead to reversible and irreversible behavior
in amorphous solids.
