Best Connected Individuals Are Not the Most Influential in Social Networks
technologyreview.com
technologyreview.com
That is, you can be a hub in a low k-shell, if say, you live in a town where everyone knows everyone but only the mailman ever leaves town.
Edit: in other words, this says that it's not about how many people you know, but how many highly-connected people you know. That's exactly what is usually informally meant by "well-connected".
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."
I don't find that easy to imagine at all. Social systems are full of rules.