  Who are the influential people in an online social network? The answer to
this question depends not only on the structure of the network, but also on
details of the dynamic processes occurring on it. We classify these processes
as conservative and non-conservative. A random walk on a network is an example
of a conservative dynamic process, while information spread is
non-conservative. The influence models used to rank network nodes can be
similarly classified, depending on the dynamic process they implicitly emulate.
We claim that in order to correctly rank network nodes, the influence model has
to match the details of the dynamic process. We study a real-world network on
the social news aggregator Digg, which allows users to post and vote for news
stories. We empirically define influence as the number of in-network votes a
user's post generates. This influence measure, and the resulting ranking,
arises entirely from the dynamics of voting on Digg, which represents
non-conservative information flow.
  We then compare predictions of different influence models with this empirical
estimate of influence. The results show that non-conservative models are better
able to predict influential users on Digg. We find that normalized
alpha-centrality metric turns out to be one of the best predictors of
influence. We also present a simple algorithm for computing this metric and the
associated mathematical formulation and analytical proofs.
