graph - floyd warshall running time complexity in terms of edges -

express running time Θ() of floyd-warshall algorithm pairs shortest path problem graph g(v, e): i. in terms of number of vertices v in g. ii. in terms of number of edges e in dense graph g. iii. in terms of number of edges e in sparse graph g.

for number i. o(v^3) . ( correct me if im wrong ). number ii , iii. not find way it. still o(e^3) both?

in standard implementation of floyd-warshall algorithm, there 3 nested loops run through vertices of graph. gives time complexity of o(v^3) said, , independent of size of e.

if define dense graph 1 e ~ v^2 , sparse graph 1 e ~ v, answers (ii) , (iii) o(e^(3/2)) , o(e^3) respectively.