Topological descriptions are an attractive alternative to conventional
crystallographic formalism for describing crystals and are essential
for describing aperiodic states lacking long-range translational and o
rientational order. In networks, topological connectivity approaches a
re usefully applied in making assessments of glass-forming ability and
in providing a local description of network structure which can asses
s extendability. The structural freedom required to form aperiodic net
works is directly related to connectivity, and the range of allowable
structural possibilities can be enumerated using combinatorial geometr
y. Detailed applications to periodic and aperiodic network silicas are
reviewed.