Caterpillar Cowboy

The importance of hubs may have been overstated, say Kitsak and pals. “In contrast to common belief, the most influential spreaders in a social network do not correspond to the best connected people or to the most central people,” they say.

At first glance this seems somewhat counterintuitive but on reflection it makes perfect sense. Kitsak and co point out that there are various sceanrios in which well connected hubs have little influence over the spread of infromation. “For example, if a hub exists at the end of a branch at the periphery of a network, it will have a minimal impact in the spreading process through the core of the network.”…

The question then is how to find these influential individuals. Kitsak and co say that the way to do this is to study a quantity called the network’s “k-shell decomposition”. That sounds complicated but it isn’t: a k-shell is simply a network pruned down to the nodes with more than k neighbours. Individuals in the highest k-shells are the most influential spreaders.