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Recursive Solution

d_ij^(m) = weight of path from i to j containing at most m edges
$d_{ij}^{(0)} \;=\; \left\{ \begin{array}{ccc} 0 & {\rm if} & i=j \\ \infty & {\rm if} & i \neq j \\ \end{array} \right.$
$d_{ij}^{(m)} \;=\; \min_{1 \leq k \leq n} \{d_{ik}^{(m-1)} \;+\; w_{kj}\} \;\;\;m \geq 1, \;n=\mid V \mid$
$\delta(i,j) \;=\; d_{ij}^{(n-1)} \;=\; d_{ij}^{(n)} \;=\; d_{ij}^{(n+1)} \;=\; ..$
There are at most n-1 edges in the shortest path from i to j assuming no negative weight cycles.

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