(ii) Algorithms based on all-pairs shortest paths
: the method developed by  adopted modification of algorithms like the Floyd-Warshall [55, 59, 60] to enable parallelism and space-efficiency in calculation of the BC.
Betweenness centrality  of a node v is the sum of the fraction of all-pairs shortest paths
that pass through v:
The shortest path problem can be classified as SSSTSP (single-source single-target shortest path), SSMTSP (single-source many-target shortest paths), APSP (all-pairs shortest paths
), and kSP (k shortest paths).
Betweenness centrality of a node i can be defined as sum of the fractions of all-pairs shortest paths
that passes through i.
In particular, the problem of computing and updating efficiently all-pairs shortest paths
in a distributed network whose topology dynamically changes over the time is considered crucial in today's communication networks.
Pal, An optimal algorithm for solving all-pairs shortest paths
on trapezoid graphs, International Journal of Computational Engineering Science, 3 (2)(2002) 103-116.