See also this HN submission for the original article: <a href="http://news.ycombinator.com/item?id=1097567" rel="nofollow">http://news.ycombinator.com/item?id=1097567</a><p>Figure 1d in the linked-to paper illustrates the difference between high k-shell and high k nicely.<p>To quote from the paper (where k = # of edges a node has): "We start by removing all nodes with degree k = 1. After removing all 
the nodes with k = 1, some nodes may be left with one link, so we continue pruning the 
system iteratively until there is no node left with k = 1 in the network. The removed nodes, 
along with the corresponding links, form a k-shell with index kS = 1. In a similar fashion, 
we iteratively remove the next k-shell, kS = 2, and continue removing higher k-shells until 
all nodes are removed. As a result, each node is associated with a unique kS index, and the 
network can be viewed as the union of all k-shells."