The paper focuses on the characteristic local network structure of icosahedra observed in the relaxed amorphous metals and its contribution to their elastic properties. Using molecular dynamics method, CuxZr100-x binary amorphous models are constructed by rapidly quenching process from liquid. Voronoi polyhedron analyses expose the existence of the medium-range local network structure composed of inter-penetrating icosahedra. It is found that the globally averaged shear modulus obtained from the atomistically defined elastic moduli decreases with increasing free volume content in the condensed matter. The contribution of the densely packed icosahedral cluster with higher elastic rigidity to the global elastic modulus is discussed.