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Manolis,

You might want to have a look at this blog post (http://wp.me/poFcY-2O) for 
calculating the length of the shortest paths using Dijkstra's algorithm. Brandes 
(2001) suggested to use Dijkstra's algorithm when calculating betweenness in 
weighted networks; and Newman (2001) used it when calculating closeness in 
weighted networks.

Best,

Tore

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