  We study theoretically "graphene-like" plasmonic metamaterials constituted by
two-dimensional arrays of metallic nanoparticles, including perfect honeycomb
structures with and without inversion symmetry, as well as generic bipartite
lattices. The dipolar interactions between localised surface plasmons in
different nanoparticles gives rise to collective plasmons that extend over the
whole lattice. We study the band structure of collective plasmons and unveil
its tunability with the orientation of the dipole moments associated with the
localised surface plasmons. Depending on the dipole orientation, we identify a
phase diagram of gapless or gapped phases in the collective plasmon dispersion.
We show that the gapless phases in the phase diagram are characterised by
collective plasmons behaving as massless chiral Dirac particles, in analogy
with electrons in graphene. When the inversion symmetry of the honeycomb
structure is broken, collective plasmons are described as gapped chiral Dirac
modes with an energy-dependent Berry phase. We further relax the geometric
symmetry of the honeycomb structure by analysing generic bipartite hexagonal
lattices. In this case we study the evolution of the phase diagram and unveil
the emergence of a sequence of topological phase transitions when one hexagonal
sublattice is progressively shifted with respect to the other.
