Floyd-Warshall is initialized with dist[u][u] = 0 , can we do dist[u][u] = INF and run a default implementation of Floyd-Warshall hoping that dist[u][u] is the shortest distance from u to u? (i.e the minimum weight cycle)?

Does this works for both directed and undirected graphs?

I'm taking for a default implementation something like wikipedia:

1 let dist be a |V| × |V| array of minimum distances initialized to ∞ (infinity) 2 for each vertex v 3 dist[v][v] ← 0 4 for each edge (u,v) 5 dist[u][v] ← w(u,v) // the weight of the edge (u,v) 6 for k from 1 to |V| 7 for i from 1 to |V| 8 for j from 1 to |V| 9 if dist[i][j] > dist[i][k] + dist[k][j] 10 dist[i][j] ← dist[i][k] + dist[k][j] 11 end if