Abstract DC electrical conductivity and elastic moduli of cubic samples made of two kinds of compressed expanded graphite are measured as a function of their apparent density. Different percolation thresholds at which the physical properties under study are found to vanish are determined. The accuracy of the values is confirmed by the application of the usual scaling laws above but near these thresholds: the corresponding critical exponents are indeed found to be very close to their universal values. The relationships between the connectivity d c (i.e., scalar) and rigidity d r (i.e., vectorial) critical densities are discussed. It is shown that the ratio d r/ d c is always almost equal to 8/5, which fact may be accounted by the so-called Kirkwood–Keating (KK) model. To our knowledge, it is the first time that such a constant value is observed in real materials. The KK model is also consistent with critical exponents of elasticity found in both kind of samples. Hence, compressed expanded graphite appears to behave like a disordered heterogeneous medium in which elastic forces are mostly of central nature but include also bond-bending contributions.