  Many popular measures used in social network analysis, including centrality,
are based on the random walk. The random walk is a model of a stochastic
process where a node interacts with one other node at a time. However, the
random walk may not be appropriate for modeling social phenomena, including
epidemics and information diffusion, in which one node may interact with many
others at the same time, for example, by broadcasting the virus or information
to its neighbors. To produce meaningful results, social network analysis
algorithms have to take into account the nature of interactions between the
nodes. In this paper we classify dynamical processes as conservative and
non-conservative and relate them to well-known measures of centrality used in
network analysis: PageRank and Alpha-Centrality. We demonstrate, by ranking
users in online social networks used for broadcasting information, that
non-conservative Alpha-Centrality generally leads to a better agreement with an
empirical ranking scheme than the conservative PageRank.
