Set new edge capacity

Question

Bug introduced in 9.0 or earlier and fixed in 12.0

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I am trying to add a new edge to an existing graph and set its capacity, but for some reason the SetProperty call is not evaluated. A minimal example:

g = Graph[{1 -> 2, 2 -> 3}, EdgeCapacity -> {10, 20}];
gt = EdgeAdd[g, 1 -> 3];
gt = SetProperty[{gt, 1 -> 3}, EdgeCapacity -> 10]

(* Out: SetProperty[{*graph with new edge pic*, 1 -> 3}, EdgeCapacity -> 10]*)

However, if I call SetProperty with EdgeWeight or EdgeLabels instead, it works fine. What is the proper way to set a new edge capacity?

I am using version 10.3.0.

Answer 1

This is not an answer, just an analysis of the problem.

Mathematica stores different edge properties in different ways.

EdgeWeight, EdgeCost and EdgeCapacity seem to be stored as a plain list of numbers, set in a separate option of Graph. They are all affected by this problem.

What happens when using EdgeAdd is that this list is not amended:

gt // InputForm

Graph[{1, 2, 3}, {DirectedEdge[1, 2], DirectedEdge[2, 3], DirectedEdge[1, 3]}, 
 {EdgeCapacity -> {10, 20}}]

It still has length 2, even though the graph now has three vertices.

I would have expected EdgeCapacity -> {10, 20, 1}, as 1 is the default value of this property.

This way EdgeAdd essentially corrupts the internal structure of the Graph and makes it unsafe to use. All sorts of unexpected things may happen when trying to use weighted graph functions on it (typically they just don't evaluate).