Question about the meaning of the term 'weight' in computation of betweenness centrality
I'm new to graph-tool, and I have a question about how the betweenness centrality measure for weighted graphs is being computed. (I apologize in advance if this is a dumb question).
My question is about how path lengths between pairs of nodes in the computation of betweenness centrality are computed for weighted graphs - is the distance between two nodes computed as the sum of the edge weights along a path between them, as described in the reference [brandes-faster-2001]? I interpret the term 'weight' in the context of a network as a measure of some kind of connectedness between nodes, where larger weight values correspond to stronger connections. If path length in the weighted graph is computed as the sum of these weights, then pairs of nodes connected by edges with larger weight values will appear 'farther' away from each other than those with smaller edge weights, which is the opposite of the result I would expect. Should I be inverting my edge weight values before passing them to the centrality modules? i.e. should I interpret the concept of edge weight as a measure of difference rather than similarity in this toolbox?
Thanks!