  The interaction between doped graphene nanoislands connected by narrow
junctions constitutes an ideal testbed to probe quantum effects in plasmonic
systems. Here, the interaction between graphene plasmons in neighboring
nanoislands is predicted to be extremely sensitive to the size and shape of the
junctions. The reported {\it ab initio} calculations reveal three different
regimes of interaction: (1) for narrow bridges ($<4$ carbon-atom rows), the
conductance of the junction is too low to allow electron transport and the
optical response is dominated by a characteristic bonding dipolar dimer mode
that also appears in a classical description; (2) for wider junctions (4-8
carbon rows), a strong charge polarization is induced across the junction,
which gives rise to a novel {\it junction plasmon} that has no counterpart in a
classical description; (3) for even wider junctions ($\ge8$ rows), their
conductance is sufficiently large to allow charge transport between the two
graphene islands, resulting in a pronounced charge-transfer plasmon, which can
also be described classically. This work opens a new path for the investigation
of intrinsic plasmon quantum effects.
