Site percolation in random networks

The site-percolation threshold has been calculated for randomly coordinated networks based on a model of computer-generated randomly packed hard spheres (RPHS). Each network is generated by allowing each sphere to coordinate to (i.e., be in contact with) every other sphere up to a given coordinating radius $r$, and the percolation threshold is calculated for different values of $r$. When the percolation threshold is plotted against the reciprocal of the coordination number, the results are well described by two straight lines intersecting at a point corresponding to a coordination number of 12, in agreement with results of regular lattices. It is suggested that this result forms a useful empirical rule for site percolation in random networks with applications in, for example, random particulate systems.