  We model black hole microstates and quantum tunneling transitions between
them with networks and simulate their time evolution using well-established
tools in network theory. In particular, we consider two models based on
Bena-Warner three-charge multi-centered microstates and one model based on the
D1-D5 system; we use network theory methods to determine how many centers (or
D1-D5 string strands) we expect to see in a typical late-time state. We find
three distinct possible phases in parameter space for the late-time behaviour
of these networks, which we call ergodic, trapped, and amplified, depending on
the relative importance and connectedness of microstates. We analyze in detail
how these different phases of late-time behavior are related to the underlying
physics of the black hole microstates. Our results indicate that the expected
properties of microstates at late times cannot always be determined simply by
entropic arguments; typicality is instead a highly non-trivial, emergent
property of the full Hilbert space of microstates.
