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And if you need dynamic graph with variable weighting and nodes, that's a case for D*

Mostly used for drone/rover/robot navigation in open environments, with the graphs evolving as the robot discover the environment.

https://en.wikipedia.org/wiki/D*

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Only if the area changing is near the start of the search, not near the goal. (i.e. near the sensors of a mobile robot, rather than near the destination far from the robot).

D* can be pathologically slower than repeated A* searches under such conditions.

I've been using a modified D*. It increases the grid size as the path moves out of the robot's observable area. This allows a fast search even when the goal is in a environment with known dynamic obstacles.

Ideally speaking, you need to plan in higher dimensions to get an optimal path in dynamic environments

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