Network integrity and non-random removal of nodes

On 20 Nov 2002, William Waites wrote:

If you randomly select nodes to remove, by the time you have removed 25% of them, the network breaks up into many isolated islands.

One of the key points was the nodes were removed in ranked order, not in random order. Removing the nodes in ranked order result in a linear decrease in connectivity, i.e. remove the top 1% of the core nodes removes 1% of the connections. But then the scary academic language appears "the curves appear to be highly asymmetric around a critical point." That is an understatement like "Houston, we have a problem." http://www.caida.org/outreach/papers/2001/OSD/ Its a very interesting paper, and I recommend anyone responsible for network integrity or reliability read it.