A paper called “Identifying influential spreaders in complex networks” by Kitsak et al. really caught my interest today. They demonstrate that the most social individuals in a population are not the most efficient spreaders of information. If you’re leading social media campaigns right now, you should definitely read this paper.
It isn’t idiotic to assume that the most connected individuals create meaningful hubs which are information rich and that this information gets spread efficiently throughout the network. However now that there is some science to help us see clear, we no longer need to assume these things. Let’s take a look at their findings (in short):
“Networks portray a multitude of interactions through which people meet, ideas are spread, and infectious diseases propagate within a society. Identifying the most efficient “spreaders” in a network is an important step to optimize the use of available resources and ensure the more efficient spread of information. Here we show that, 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 (high betweenness centrality).
Instead, we find:
(i) The most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis.
(ii) When multiple spreaders are considered simultaneously, the distance between them becomes the crucial parameter that determines the extend of the spreading. Furthermore, we find that– in the case of infections that do not confer immunity on recovered individuals– the infection persists in the high k-shell layers of the network under conditions where hubs may not be able to preserve the infection. Our analysis provides a plausible route for an optimal design of efficient dissemination strategies.”
So basically, we can say that:
- if a hub exists at the end of a branch at the periphery of a network, it will have very little impact in the spreading of information through the core of the network.
- if a person is positioned more towards the core of the network, even if they are much less well connected, their information dissemination powers are substantial.
To find those individuals:
You use the k-shell decomposition algorithm which is the process of pruning a network down to nodes that have more than k-neighbours. All of the nodes in the highest k-shells represent the influential members of a social network.
1) All nodes with degree k=1 are removed
2) The removed nodes along with the links connecting them form the kS = 1 k-shell
3) Prune all nodes of degree k=2 to extract the kS = 2 k-shell
4) Keep on with this process until all higher values of k are removed
After this process you can see the network as a set of adjacent k-shells (on page 19 of the paper you will find a useful illustration)
So?
This means that having 17,000+ followers on Twitter does make someone influential. It’s more about strategy than numbers. Who do you know? How’s your k-shell looking? 
Well… on the other hand big followers number can still be valuable. May be just to generate a sharp and sudden peak of traffic… still useful.
I think that the quality of the followers is important. Better to have 10 followers who engage with your product/service/whatever than 20,000 who ignore you.