You can find a PDF version of this blog post here. A weighted graph is a data structure consisting of some vertices and edges, and each edge has an associated cost of traversal. Let's suppose we want to compute the shortest distance from vertex $u$ to every other vertex $v$ in the graph, and we express this cost function as $\mathcal{L}_u(v)$. For example, if each edge in this graph has cost $1$,
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