Nice musings by chum David C and Stowe Boyd around this study that suggests it's the not the number of connections you have that determines your influence, but rather the nature of those connections - your "betweenness" as Stowe calls it:
"It is not your follower count, or who you follow, per se. But, instead, do you have short paths into other social scenes, both incoming and outgoing? That is the deep structure of being truly connected: bridging over different social scenes, acting as a conduit, a vector, a filter and amplifier for ideas good and bad, the best insights, and deadly viruses." [SB]
But David makes this important point:
"Influence is fluid. It resides less in the node and more in the interactions between the nodes. It is the interactions which change the state of the group, not a change in the condition of the nodes (think water H2O molecules and ice, water, steam...
...This means that giving interesting things to people to do together - bringing them together around things they care about (through shared purpose), to act on those things, has more value than spotting the influencer and giving them some sort of message you expect them to go off and influence others with"
Which prompts my sixpenceworth:
Influence is not something done by certain people to other people (as for example the pic above from New Scientist might suggest) it's the result of those people we call The Influenced doing something in response to those we call Influential.
As Duncan Watts and Matt Salganik noted in their important music-download paper, it's more about the readiness of a population to adopt a behaviour than the behaviour of specific individuals.
I.e. The Influenced do the heavy lifting of Influence, not the Influentials - and the fact that Influence is often mutual i.e. we all (well-connected or not) take cues from each other - that's one important reason why the search for the Influentials is so prone to misunderstanding and dead-ends.
As soon as we grasp this, going about understanding and harnessing influence begins to be a little more sensible...