CODEWITHSUNDEEP
c++classgraph
Nathan Lu
Nathan Lu

Reputation: 69

When adding a vertex to a weighted undirected graph, which weight stays?

I'm doing an adjacency list implementation of a graph class in C++ (but that's kinda irrelevant). I have a weighted directionless graph and I am writing the addVertex method. I have basically everything down, but I'm not sure what I should do when I add a vertex in between two others that were already there and had their own corresponding weights.

Should I just throw away the old weight that the vertex stored? Should I use the new one that was passed in? A mix of both? Or does it not matter at all what I pick?

I just wanted to make sure that I was not doing something I shouldn't.

Thanks!

Upvotes: 0

Views: 145

Answers (1)

StephanH
StephanH

Reputation: 470

I guess it depends on what you want to achieve. Usually, an adjacency list is a nested list whereby each row i indicates the i-th node's neighbourhood. To be precise, each entry in the i-th node's neighbourhood represents an outgoing connection from node i to j. The adjacency list does not comprise edge or arc weights.

Hence, adding a vertex n should do not affect the existing adjacency list's entries but adds a new empty row n to the adjacency list. However, adding or removing edges alter the adjacency list's entries. Thus, adding a vertex n "between two other [nodes i and j] that were already there and had their own corresponding weights" implies that you remove the existing connection between i and j and eventually add two new connections (i,n) and (n,j). If there are no capacity restrictions on the edges and the sum of distances (i,n) and (n,j) dominates the distance (I,j) this could be fine. However, if the weights represent capacities (e.g. max-flow problem) you should keep both connections.

So your question seems to be incomplete or at least unprecise. I assume that your goal is to calculate the shortest distances between each pair of nodes within an undirected graph. I suggest keeping all the different connections in your graph. Shortest path algorithms can calculate the shortest connections between each node pair after you have finished your graph's creation.

Upvotes: 1

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