Figure 1d in the linked-to paper illustrates the difference between high k-shell and high k nicely.
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."
Figure 1d in the linked-to paper illustrates the difference between high k-shell and high k nicely.
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."