  The problem of continuum percolation in dispersions of rods is reformulated
in terms of weighted random geometric graphs. Nodes (or sites or vertices) in
the graph represent spatial locations occupied by the centers of the rods. The
probability that an edge (or link) connects any randomly selected pair of nodes
depends upon the rod volume fraction as well as the distribution over their
sizes and shapes, and also upon quantities that characterize their state of
dispersion (such as the orientational distribution function). We employ the
observation that contributions from closed loops of connected rods are
negligible in the limit of large aspect ratios to obtain percolation thresholds
that are fully equivalent to those calculated within the second-virial
approximation of the connectedness Ornstein-Zernike equation. Our formulation
can account for effects due to interactions between the rods, and many-body
features can be partially addressed by suitable choices for the edge
probabilities.
