Random removal of edges from scale free graphs

It has been discovered that many naturally occurring networks (the internet, the power grid of the western US, various biological networks, etc.) satisfy a power-law degree distribution. Such scale-free networks have many interesting properties, one of which is robustness to random damage. This problem has been analyzed from the point of view of node deletion and connectedness. Recently, it has also been considered from the point of view of node deletion and scale preservation. In this paper we consider the problem from the point of view of edge deletion and scale preservation. In agreement with the work on node deletion and scale preservation, we show that a scale-free graph should not be expected to remain scale free when edges are removed at random.