We propose a measurable parameter H quantifying the halo nature of one-neutron halo nuclei (a) and investigate the properties of H, assuming the core + neutron (c + n) model for a. The parameter H is defined by H = [sigma(abs)(a) - sigma(abs)(c)]/sigma(abs)(n) with directly measurable absorption cross sections sigma(abs) of a, c, and n scattering at the same incident energy per nucleon. It varies with the one-neutron separation energy S-n in a range of 0 <= H <= 1, and the halo structure is most developed when H = 1. This situation is realized only for s-wave halo nuclei in the S-n = 0 limit. We consider Be-11 and C-15,C-19 as s-wave halo nuclei, Ne-31 and Mg-37 as p-wave halo nuclei, and C-17 as an example of d-wave nonhalo nuclei. For each of halo nuclei, the value of H is deduced at a measured S-n from measured total reaction cross sections for c, n, and a scattering at intermediate and high incident energies where projectile breakup effects are negligible. The location of the resulting (S-n, H) is plotted in the S-n- H plane. The empirical values of H at the measured S-n are extrapolated to small S-n with model calculations based on the eikonal + adiabatic approximation. In the S-n-H plane, the model lines are well separated into three groups of s-wave halo, p-wave halo, and d-wave nonhalo particularly in the vicinity of S-n = 0, and the s-wave halo lines are always above the other lines, since only the s-wave halo lines can reach a point (S-n, H) = (0,1) independently of the concrete form of the interaction between c and n. The relation among the three kinds of lines may be universal for any halo nucleus with small Sn. The point (S-n, H) = (0,1) can be regarded as a scale-invariant point in the sense that the z-integrated neutron density characterizing halo structure is invariant under the scale transformation there.