feat: assign weights in graph

[miparnisari]

Description

This is the scaffolding code required to compute weights for each node and edge. It's not meant to support every kind of model - more followup PRs will come. (For example, models with cycles are not handled).

Please review each model in the weighted_graph_builder_test.go and visualize the output in https://dreampuf.github.io/GraphvizOnline/. This will help you review the correctness of the weight assignment algorithm.

Example

[adriantam]

May not be for this PR. But it will be good idea to add unit test in some of the major method as there may be cases not covered in the TestWeightedGraphBuilder test

[elbuo8]

Why not use gonum's weighted graph? 🤔

[elbuo8]

Why not use the existing builder?

[miparnisari]

The existing builder's job is to figure out the edges, their directions, etc. This builder's job is to assign weights. Since both are fairly complex jobs i'd like to keep them separate. Makes testing easier and less code per file

[miparnisari]

Why not use gonum's weighted graph? 🤔

@elbuo8 several reasons:

1. gonum's weighted graph allows natively assigning weights to edges only
2. those weights are float64 only: https://pkg.go.dev/gonum.org/v1/gonum/graph#WeightedLine

[senojj]

Non-Blocking

The relationship between the weighted graph builder and the weighted graph is a bit odd. Currently the weighted graph has a dependency of its builder, which seems backwards.

Instead of coupling it all together with the current approach:

weightedGraph, err := NewWeightedAuthorizationModelGraph(model)

I would suggest decoupling them explicitly:

weightedGraphBuilder := NewWeightedAuthorizationModelGraphBuilder()
weightedGraph, err := weightedGraphBuilder.Build(model)

I know this is introducing an additional step/line of code, however I really don't see the point of having the builder, otherwise.

[senojj]

Put in other words, is this an edge that connects a vertex to itself?

  graph TD;
      A-->A;

Loading

[miparnisari]

Yep! not sure what to call it