The Costly Path from Percolation to Full Connectivity

Requiring all nodes of a wireless multihop network to be connected is expensive and results in a poor scalability of properties such as transport capacity. We show however that it is no longer the case if we only slightly loosen the connectivity requirement, by just imposing that most nodes be connected to each other (so that the network percolates). This feature is found in models neglecting interferences, taking interferences as noise or taking a more information theoretic approach.