# How to work with JuMP and Graphs.jl

**URL:** <https://discourse.julialang.org/t/how-to-work-with-jump-and-graphs-jl/118948>\
**Category:** Optimization (Mathematical)\
**Tags:** graphs\
**Created:** [September 2, 2024, 1:45pm UTC](https://discourse.julialang.org/t/how-to-work-with-jump-and-graphs-jl/118948 "2024-09-02T13:45:05Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![mike\_k](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mike_k/32/211864_2.png) [@mike\_k](https://discourse.julialang.org/u/mike_k)\
**Post date:** [September 2, 2024, 1:45pm UTC](https://discourse.julialang.org/t/how-to-work-with-jump-and-graphs-jl/118948/1 "2024-09-02T13:45:05Z")

</div>

I try to build a flow model using JuMP and (Meta)Graphs.jl. In particular I fail to index the variables. Here is an MWE:

```julia
using Graphs
using JuMP

g = SimpleDiGraph(4)
for i in 1:3
    add_edge!(g, i, i+1)
end

model = Model()
T = 1:2
@variable(model, x[a in edges(g), t in T], Bin)
@constraint(model, x[Edge 1 => 2, 1] == 1) # error
@constraint(model, x[(2,3),1] == 1) # error

```

I tried several combinations, but always failed. As workaround, I could convert the edges as tuples, e.g.,

```julia
E = [(src(a), dst(a)) for a in edges(g)]
@variable(model, x[a in E, t in T], Bin)
@constraint(model, f[(2,3),1] == 1) # works

```

but can’t I use the edges from `g` directly? Unfortunately, I did not find any examples in which JuMP is used together with objects from (Meta)Graphs.jl. Or is doing this a bad practice at all?

---

<div class="post-metadata">

**Author:** ![filchristou](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/filchristou/32/26760_2.png) [@filchristou](https://discourse.julialang.org/u/filchristou)\
**Post date:** [September 2, 2024, 2:38pm UTC](https://discourse.julialang.org/t/how-to-work-with-jump-and-graphs-jl/118948/2 "2024-09-02T14:38:32Z")

</div>

It’s useful to also show the errors you get.

In that case I think you need to do

```julia
@constraint(model, x[Edge(1 => 2), 1] == 1)

```

As far as I know JuMP cannot understand Graphs.jl so you have to give it the numbers. Use `get_prop!` from MetaGraphs.jl for that.

Probably a good resource is [GitHub - JuliaGraphs/GraphsOptim.jl: A package for graph optimization algorithms that rely on mathematical programming.](https://github.com/JuliaGraphs/GraphsOptim.jl)  
Have a look at the source code to see how they define models.

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [September 2, 2024, 9:33pm UTC](https://discourse.julialang.org/t/how-to-work-with-jump-and-graphs-jl/118948/3 "2024-09-02T21:33:46Z")

</div>

@filchristou is correct.

Your set is `edges(g)`, so the keys are the elements of that set.

```Julia
julia> using Graphs, JuMP

julia> g = SimpleDiGraph(4)
{4, 0} directed simple Int64 graph

julia> for i in 1:3
           add_edge!(g, i, i+1)
       end

julia> model = Model();

julia> @variable(model, x[edges(g), 1:2], Bin)
2-dimensional DenseAxisArray{VariableRef,2,...} with index sets:
    Dimension 1, Graphs.SimpleGraphs.SimpleEdge{Int64}[Edge 1 => 2, Edge 2 => 3, Edge 3 => 4]
    Dimension 2, Base.OneTo(2)
And data, a 3×2 Matrix{VariableRef}:
 x[Edge 1 => 2,1] x[Edge 1 => 2,2]
 x[Edge 2 => 3,1] x[Edge 2 => 3,2]
 x[Edge 3 => 4,1] x[Edge 3 => 4,2]

julia> x[Edge(1 => 2), 1]
x[Edge 1 => 2,1]

```

Your `Edge 1 => 2` attempt came because Graphs for some reason has overloaded `Base.show` to remove the parentheses…

```julia
julia> Edge(1 => 2)
Edge 1 => 2

```

JuMP does’t now about Graphs.jl, so we just print what we get given.