  We study the ground-state spatial heterogeneities of the Edwards-Anderson
spin-glass model with both bimodal and Gaussian bond distributions. We
characterize these heterogeneities by using a general definition of bond
rigidity, which allows us to classify the bonds of the system into two sets,
the backbone and its complement, with very different properties. This
generalizes to continuous distributions of bonds the well known definition of a
backbone for discrete bond distributions. By extensive numerical simulations we
find that the topological structure of the backbone for a given lattice
dimensionality is very similar for both discrete and continuous bond
distributions. We then analyze how these heterogeneities influence the
equilibrium properties at finite temperature and we discuss the possibility
that a suitable backbone picture can be relevant to describe spin-glass
phenomena.
