  We examine the standard model of many-body localization (MBL), i.e., the
disordered chain of interacting spinless fermions, by representing it as the
network in the many-body (MB) basis of noninteracting localized Anderson
states. By studying eigenstates of the full Hamiltonian, for strong disorders
we find that the dynamics is confined up to very long times to disconnected MB
clusters in the Fock space. By keeping only resonant contributions and
simplifying the quantum problem to rate equations (REs) for MB states, in
analogy with percolation problems, the MBL transition is located via the
universal cluster distribution and the emergence of the macroscopic cluster. On
the ergodic side, our approximate RE approach to the relaxation processes
captures well the diffusion transport, as found for the full quantum model. In
a broad transient regime, we find an anomalous, i.e., subdiffusivelike,
transport, emerging from weak links between MB states.
