How to simulate breaking graph vertices?

Question

C++ / C#

There is a task where you need to make a program that, using algorithms, calculates the shortest path from a point to a point in a graph, one of the points asks you to make an imitation of a break in some graph vertices and recalculate the paths. Please tell me how this can be implemented.

Answer 1

You must either remove a vertex from the graph, or mark it as deleted, and in your pathfinding algorithm, simply skip such marked vertices in all cycles over the vertices.