Say that I have a directed graph reflected by the following edgelist:
1 2
1 3
2 4
3 1
3 4
I wish to calculate the betweenness centrality of this graph. Note that there are two parallel edges between point 1 and point 3.
Should the betweenness here be calculated any differently from if I instead had the following edgelist?
1 2
1 3
2 4
3 4
The general definition of betweenness centrality (of a node k) is the share of shortest path's between any two nodes i and j (where neither i nor j is the node k) that pass through node k in the total such shortest paths. (See for instance the respective wikipedia article)
As you can see, in your directed graph the shortest path from 3 to 2 passes through 1 if you include the edge 3->1 (while such a shortest path from 3 to 2 does not exist if you leave it out) thereby changing the betweenness centrality of node 1 (compared to if you leave that edge out).