We define an infinite sequence of invariants μ¯\sbK of connected, finite graphs K. These invariants detect whether or not a "longitude" associated to a cycle in K lies in the n\spth term of the lower central series of π\sb1(S\sp3−K,p). In certain cases, these invariants can be compared to Milnor's μ¯-invariants associated to links contained in K, and are found to be more discriminating.