  Graphene nanoribbons are quasi-one-dimensional meterials with finite width.
Characterizing a wide class of nanoribbons by edge shape and width, we make a
systematic analysis of their electronic properties. The band gap structure of
nanoribbons is shown to exhibit a valley structure with stream-like sequences
of metallic or almost metallic nanoribbons. Among them, all zigzag nanoribbons
are metallic, and armchair nanoribbons are metallic by period of 3. We find
that these stream-like sequences correspond to equi-width curves, and that the
band gap of chiral and armchair nanoribbons oscillate as a function of the
width. Furthermore a possible application of nanoribbons to nanoelectronics is
discussed.
