I read Zhang's paper Expert Finding in A Social Network, formula(1) is a propagation-base approach,similar to a standard belief propagation.Is there a code example or tool to do this? the propagation scheduler seems need to be a parallel implementation.Any guidance would be greatly appreciated.
a simple standard belief propagation
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You might want to check out LibDai (open source, based on C++ and MatLab) which provides some inference algorithms, including some variations of the belief propagation.