  We study the spectral properties of infinite rectangular quantum graphs in
the presence of a magnetic field. We study how these properties are affected
when three-dimensionality is considered, in particular, the chaological
properties. We then establish the quantization of the Hall transverse
conductivity for these systems. This quantization is obtained by relating the
transverse conductivity to topological invariants. The different integer values
of the Hall conductivity are explicitly computed for an anisotropic diffusion
system which leads to fractal phase diagrams.
