The study of social networks has thrown up more than a few surprises over the years. It's easy to imagine that because the links that form between various individuals in a society are not governed by any overarching rules, they must have a random structure. So the discovery in the 1980s that social networks are very different came as something of a surprise. In a social network, most nodes are not linked to each other but can easily be reached by a small number of steps. This is the so-called small worlds network.
Today, there's another surprise in store for network connoisseurs courtesy of Maksim Kitsak at Boston University and various buddies. One of the important observations from these networks is that certain individuals are much better connected than others. These so-called hubs ought to play a correspondingly greater role in the way information and viruses spread through society.
In fact, no small effort has gone into identifying these individuals and exploiting them to either spread information more effectively or prevent them from spreading disease.
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 scenarios 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."
By contrast, "a less connected person who is strategically placed in the core of the network will have a significant effect that leads to dissemination through a large fraction of the population."
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.
The team has tested the idea on a number of networks including the network formed by 5.5 million members of LiveJournal.com, the network of email contacts in the computer science department at University College London and the network of actors who have co-starred in adult films as defined by the internet movie database.
Perhaps the most interesting outcome is that the new approach emphasises the location of the individual within the network relative to the information or virus that is being spread. In hindsight, that seems like an obvious point but one that has not been well accounted for in the past.
The team also use their new ideas to study the spread of infections which do not confer immunity on recovered individuals. They conclude that "high k-shell layers form a reservoir where infection can survive even if its contagiousness is well below the epidemic threshold." Not an altogether reassuring result.
Ref: arxiv.org/abs/1001.5285: Identifying Influential Spreaders in Complex Networks