Continuous deformations in random networks

We examine some current ideas concerning the differences between covalent random networks with high and low average coordination. These ideas can be made rigorous by considering the number of continuous deformations (i.e. zero frequency modes) allowed within the network. In the transition from one kind of network to another, rigidity percolates through the system. This leads to a picture in which random networks with low average coordination (polymeric glasses) have large floppy or spongy regions with a few rigid inclusions. On the other hand in random networks with high average coordination (amorphous solids) the rigid regions have percolated to form a rigid solid with a few floppy or spongy inclusions.