Shortest-path distance ($d(s,t)={\inf }_{P:s⇝t}{\sum }_{e\in P}w(e)$)

The infimum of total edge weights over allowed walks from a source to a target. The value is $+\infty$ when no route exists. A negative cycle reachable from the source and able to reach the target makes it $-\infty$. In a finite graph without such a cycle, a finite distance is attained by a graph path, after removing non-improving repetitions.