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In Newman's random walk betweenenss centrality paper (A measure of
betweenness centrality based on random walks. M. E. J. Newman.
arXiv:cond-mat/0309045 v1. 1 sep 2003.), there is notes like this in page 3
about flow betweenness centrality :
"Technically, this definition (of flow betweenness) is not unique,
because there need not be a unique solution to the flow problem. To get
around this difficulty, Freeman et al. define their betweenness measure as
the the maximum possible flow through i over all possible solutions to the
st maximum flow problem, averaged over all s and t."
Because maximum flow network is not uniquely determined, that problem is
occured. But... are there any algorithm that enable the calculation (:the
maximum possible flow through i over all possible solutions to the st
maximum flow problem) mentioned in notes? I haven't heard any comment about
the problem in algorithm courses or books.
Thank you for any comments.
Se Kwon, Kim
KAIST (Korean Advanced Institute of Science & Technology)
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