Posts tagged ‘shortest distance’

Betweenness in weighted networks

Betweenness exampleThis post highlights a generalisation of Freeman’s (1978) betweenness measure to weighted networks implicitly introduced by Brandes (2001) when he developed an algorithm for calculating betweenness faster. Betweenness is a measure of the extent to which a node funnels transactions among all the other nodes in the network. By funnelling the transactions, a node can broker. This could be by taking a cut (e.g. Ukraine controls most gas pipelines from Russia to Europe) or distorting the information being transmitted to its advantage.

The content of this post has been integrated in the tnet manual, see Node Centrality in Weighted Networks.

February 20, 2009 at 12:00 am 6 comments

Average shortest distance in weighted networks

Distance between nodesThe average distance that separate nodes in a network became a famous measure following Milgram’s six-degrees of separation experiment in 1967 that found that people in the US were on average 6-steps from each other. This post proposes a generalisation of this measure to weighted networks by building on work by Dijkstra (1959) and Newman (2001).

The content of this post has been integrated in the tnet manual, see Shortest Paths in Weighted Networks.

January 9, 2009 at 12:00 am 8 comments

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