Mass-law scaling of fractal scale-free networks under bond percolation

Fractal networks have been proposed to obey a scaling theory in which the mass of a covering box grows as [Formula: see text] in box diameter L and hub degree k, so that [Formula: see text]. We measure [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] on the same networks under bond percolation of hierarchical fractal scale-free networks with exactly known threshold and intact exponents. Fitted against hub degrees in the damaged network, [Formula: see text] falls toward the threshold, by up to [Formula: see text] and by an amount that depends on the definition of a fragmented box’s mass. For bond occupation probability [Formula: see text] this fall is mainly regression dilution from the binomial thinning of hub degrees. Against the pre-damage degree, used as an instrument, the within-level slope over levels [Formula: see text] stays between 0.97 and 1.04, under three box-mass conventions at [Formula: see text] and two at [Formula: see text] nodes. For [Formula: see text] hub degrees, surviving mass and chemical lengths approach intact scaling at large scales, consistent with the lower small-scale box dimension being a crossover. The closure of [Formula: see text] is only a weak consistency check.