How to update the graph datastructure dynamically


I have created a graph datastructure to represent a physical floor layout in using hashtables and nodes (class).

And i am applying the Dijkstra algorithm to calculate the shortest path between any two nodes which is working fine.

This datastructure has got the obstacles defined before applying the algorithm thus the obstacles are static.

I have the following questions:
1. How do i dynamically update the graph datastructure to reflect the obstacles or changes.

2. Since the changes can happen at real time, what is the thought process that should go behind calculating the Shortest Path. Because, the path calculated may not be valid with the changed graph.

Should I recreate the graph datastructure again and again because the changes are happening at realtime.

Please help..I have no clue to proceed further.

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