Within the scattering matrix approach to electronic transport, the scattering
and transport properties of tight-binding random graphs are analyzed. In
particular, we compute the scattering matrix elements, the transmission, the
channel-to-channel transmission distributions (including the total transmission
distribution), the shot noise power, and the elastic enhancement factor. Two
graph models are considered: random geometric graphs and bipartite random
geometric graphs. The results show an insulating to a metallic crossover in the
scattering and transport properties by increasing the average degree of the
graphs from small to large values. Also, the scattering and transport
properties are shown to be invariant under a scaling parameter depending on the
average degree and the graph size. Furthermore, for large connectivity and in
the perfect coupling regime, the scattering and transport properties of both
graph models are well described by the random matrix theory predictions of
electronic transport, except for bipartite graphs in particular scattering
setups.Comment: 13 pages, 16 figure