Influence Propagation: Patterns, Model and a Case Study

When a free, catchy application shows up, how quickly will people notify their friends about it? Will the enthusiasm drop exponentially with time, or oscillate? What other patterns emerge?

Here we answer these questions using data from the Polly telephone-based application, a large influence network of 72,000 people, with about 173,000 interactions, spanning 500MB of log data and 200 GB of audio data.

We report surprising patterns, the most striking of which are: (a) the Fizzle pattern, i.e., excitement about Polly shows a power-law decay over time with exponent of -1.2; (b) theRendezvous pattern, that obeys a power law (we explain Rendezvous in the text); (c) theDispersion pattern, we find that the more a person uses Polly, the fewer friends he will use it with, but in a reciprocal fashion.

Finally, we also propose a generator of influence networks, which generate networks that mimic our discovered patterns