  Graphene, with its quantum Hall topological (Chern) number reflecting the
massless Dirac particle, is shown to harbor yet another topological quantum
number. This is obtained by combining Streda's general formula for the
polarization associated with a second topological number in the Diophantine
equation for the Hofstadter problem, and the adiabatic continuity, earlier
shown to exist between the square and honeycomb lattices by Hatsugai et al.
Specifically, we can regard, from the adiabatic continuity, graphene as a
``simulator" of square lattice with half flux quantum per unit cell, which
implies that the polarization topological numbers in graphene in weak magnetic
fields is 1/2 per Dirac cone for the energy region between the van Hove
singularities, signifying a new quantum number characterizing graphene.
