This paper explores the modulus (discrete $p$-modulus) of the family of edge
covers on a discrete graph. This modulus is closely related to that of the
larger family of fractional edge covers; the modulus of the latter family is
guaranteed to approximate the modulus of the former within a multiplicative
factor based on the length of the shortest odd cycle in the graph. The bounds
on edge cover modulus can be computed efficiently using a duality result that
relates the fractional edge covers to the family of stars