  We present an edge-based framework for the study of geometric elastic network
models to model mechanical interactions in physical systems. We use a
formulation in the edge space, instead of the usual node-centric approach, to
characterise edge fluctuations of geometric networks defined in d- dimensional
space and define the edge mechanical embeddedness, an edge mechanical
susceptibility measuring the force felt on each edge given a force applied on
the whole system. We further show that this formulation can be directly related
to the infinitesimal rigidity of the network, which additionally permits three-
and four-centre forces to be included in the network description. We exemplify
the approach in protein systems, at both the residue and atomistic levels of
description.
