The accumulation of part of the algorithm is probably the most difficult. When you reach this part, you will get in sigma the number of shortest paths from the current vertex s to the remaining vertices. In addition, in Pred, you have for each vertex a list of vertices that reach them along the shortest path. The delta of the dependence will be equal to the magnitude of the internode, which will contribute to the rest of the vertices (from 0 to N-2), i.e. Depends on s of each vertex.
The vertex w is deduced from S to empty, starting with the farthest of s and ending with s itself (remember that the vertex was added to S when it was reached in the shortest path for calculating the algorithm), For each v in the list of predecessors w ( Pred [w]) a new value is calculated for the dependencies and that (for me) is the hard part.
The expression says that delta [v] = delta [v] + (sigma [v] / sigma [w]) * (1 + delta [w]), or, in other words, the new dependence for v is the dependence on what it already has a plus (sigma [v] / sigma [w]) * (1 + delta [w]). Well, first of all, note that when the vertex w is knocked out of S, its entire dependence delta [w] is calculated, because there will be no more future nodes w, therefore it cannot be in the middle of any other shortest path. Then it should be clear that (sigma [v] / sigma [w]) is the dependence of the pair (s, w) on v, i.e. Depends on the fact that the vertices s and w of v remain connected (since this is the fraction of the shortest paths from s to w passing through v). But (and this is the less obvious part, I think), the vertex v is not only in the shortest paths between s and w, but also in all the shortest paths in which w! Thus, if there was a short path from s to some vertex x passing through w, then there should be a path from s to x passing through v. Simply put, s would be more dependent on v if it depended on w. Thus, the coefficient (1 + delta [w]) is explained as follows: 1 for the dependence of v of the pair (s, w) and delta [w] on the dependence v of each pair (s, & lt, any vertex outside w>).
Finally, delta [w] is added to its total difference Cb [w] (if w == s, since s is not considered to be dependent on itself).
As I said, this is not a simple algorithm to understand at a glance. Do not rush and comment if you still have doubts.