Flow betweenness

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Origin aka Flow centrality

L.C. Freeman, White, D.R., and David Smith. 1988, Flow Centralities: Do they Predict the Economic Rise and Fall of States? - Figures INSNA Sunbelt Meetings 1988 San Diego. The flow centralities algorithm was designed by Douglas R. White who asked S.P. Borgatti to program it into UCInet.

Historical notes (DRW). This was the paper that first defined flow betweenness centrality. At that point I had given my algorithm to Borgatti and asked him to program it into UCInet. He had done so, and I had used my definition and Steve's programming of the algorithm to do the analysis in the paper. He failed to attribute the algorithm to me (and still has not done so in UciNet) and it was legitimately pounced upon by Lin Freeman, who thought it was Steve’s and took upon himself to be the “Author” with Steve of the algorithm, to be published in Social Networks. Steve didn’t have the good sense to give it proper attribution and it has become known as “UCInet’s flow betweenness algorithm.” Lin sent a copy of his paper to me as a colleague in our network program, and I said – "hey, that’s my algorithm, but Steve did not attribute it!" Lin (who had done a perfect job in explicating the algorithm) then added me as third author without attribution of authorship of the flow centrality algorithm or listing the 1988 paper.
These are minor issues although an interesting story, but when one goes to attribute the “intent” of the algorithm it is not proper to state an intent given later by Borgatti because he did not design the algorithm, he merely programmed it. You need to go back to the 1998 paper, still unpublished today, for the intent of the algorithm. My intent was precisely to measure the extent to which any node in a trade or capital flow network could “block off” the others by cutting of flow or could collect a markup on flow-through and a markdown on in-flow. The 1988 paper then used the idea of the balances between rising/falling economy, in-flow/out flow ratios that compose to index retail (large flows in divided into many small flows out) versus wholesale marketing (small flows in – underpaid – divided into a few large flows out), and also indexing “those (countries) that hold wholesale inventory and those that do not.” his produced a correct prediction about upward mobility (holding inventory in a rising economy) and downward mobility (holding inventory in a falling economy) in terms of world system position as measured by Smith and White (1991: not yet published in 1988 but already completed).
Thus, when Borgatti, Everett and Freeman (2002), Ucinet for Windows: Software for Social Network Analysis state that "Flow Betweenness has primarily been developed with information flow in mind" they are mistaken and have forgotten once again the origin of the algorithm in the 1988 paper.


Freeman, L.C., S.P. Borgatti and D.R. White, 1991. Centrality in valued graphs: a measure of betweenness based on network flow, Social Networks 13(2): 141–154. Freeman neglected to attribute the algorithm to D. R. White (1988) and failed to cite White and Smith (1988). See also Newman. Also cited in 2015. Yuxian Du, Cai Gao, Xin Chen, Yong Hu, Rehan Sadiq and Yong Deng.A new closeness centrality measure via effective distance in complex networks. Chaos 25, 033112 (2015); http://dx.doi.org/10.1063/1.4916215 Download PDF. Electronic addresses: ydeng@swu.edu.cn and prof.deng@hotmail.com

Stephen P. Borgatti. 2005 Centrality and network flow Social Networks 27(1): 55-71. Borgatti neglected to attribute the algorithm to D. R. White (1988).

Borgatti, S. P. and Everett, M.G. 2006. A graph-theoretic framework for classifying centrality measures. Social Networks 28(4): 466-484. They note p. 474:for flow betweenness: "This is really the essence of any betweenness measure: the potential for withholding flow, otherwise known as gatekeeping."


Cited Article: Centrality in valued graphs: A measure of betweenness based on network flow. Soc Netw



"...Nesta seção, serão explicadas brevemente as medidas de centralidade tradicionais que servem de referência para o presente estudo, ou seja, as centralidades de informação (degree centrality) e de autovetor (eigenvector centrality). Entretanto, como o estudo de centralidades, é fundamentado na Teoria dos Grafos (Freeman et al., 1991), serão apresentadas, primeiramente, definições básicas da Teoria dos Grafos. ..."


Luana Carneiro Brando, Renata Raposo Del-Vecchio, Joo Carlos C. B. Soares de Mello


Does not mention flow betweeness: Should move to Betweenness centrality Martin Everett, Stephen P Borgatti. 2005. Ego network betweenness. Social Networks 27(1):31-38.

Carl Nordlund