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In other words, if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?
When you start thinking about it, you understand that you need additional information about this network: how does the innovation diffuses in this network? And what are the thresholds of adoption of nodes?
Suppose, for example, that any node in this network when targeted, is able to spread a word only to it's immediate neighbours. Then targeting Diane and Ike is enough to cover the whole network.
But what if targeting a node is expensive (for example, targeting an individual means to grant her a sample of product)? Then targeting Diane is three times more effective than targeting Ike, as Diane would influence 6 people while Ike only 2. So, we can reason about the cost and effectiveness of targeting a set of nodes
If a targeted individual is able to spread a word on two steps, then Heather is the best choice, as she can reach everyone in the network in two steps.
Domingos and Richardson posed a fundamental algorithmic problem for such social network processes in this paper: "Mining the Network Value of Customers", 2001.