Finding a minimum "node" weight path Suppose a graph with node weights only (no edge weights). For a given source-sink pair, how can I find a path with the minimal sum of node weights? Does this problem have a name? Is it possible to reformulate this to a shortest-path problem?

If both nodes and edges are weighted, is it still possible to find a min-weight path?
You can treat this as a directed graph problem, where the weights of all edges coming into a node are equal to that node's weight.

If the edges are weighted too, add the node's weight and the edge's weight together to find the incoming edge's weight in the directed graph.