I was looking at this, because I wanted to convert it to Julia v1.0, but I'm not sure this function actually does what it should do.
From my understanding, it tries to solve the following (simplified here) linear program:

Given bipartite graph G with parts |V1| <= |V2|  and weightmap W = {w_ij}

maximize  Sum( x_ij * w_ij  ) where   w_ij > 0   s.t.
(I)   forall i,j     :  x_ij >= 0
(II)  forall i in V1 : Sum(x_ij) == 1 where j in neighbors(G, i)
(III) forall j in V2 : Sum(x_ij) <= 1 where i in neighbors(G, j)

There are two issues:

1. Now the objective function clearly aims to maximize the total weight. But I don't see why it only does this among the matchings with the largest number of edges. And shouldn't it be called maximum_weight_maximum_matching then? After all, the documentation suggests it looks for a maximum set of edges and not simply a maximal one.

2. Condition (II) is not possible in all cases (at least for integer solutions). For example there are bipartite graphs with parts of equal size that do not contain a perfect matching, even if the graph is connected and does not have isolated vertices.

Currently the maximum_weight_matching function doesn't work with the latest JuMP version using MOI.
I'll work on that so maybe someone can assign me to it ;)

The tag name "v0.1" is not of the appropriate SemVer form (vX.Y.Z).
cc: @matbesancon

Generator comprehension syntax used for the formulation of the objective and constraints for JuMP is deprecated and must be changed

I was trying to compute matchings with this package, I had a problem when installing the dependency BlossomV.jl (mlewe/BlossomV.jl#12). Then, I saw that the other way to solve matchings is to use mathematical programming. However, what I expected from this package was rather an implementation of the Hungarian algorithm (provided by BlossomV.jl, but not available on most platforms). Would it be possible to consider adding a pure-Julia implementation, so that it is ensured to work on all platforms? (Either coding one for this package, or using something like https://github.com/Gnimuc/Hungarian.jl or https://github.com/FugroRoames/Munkres.jl.)

The actual dictionary weights ::Dict{Edge,Int} is not flexible enough, does not allow lazy weight evaluation for instance. See JuliaGraphs/LightGraphsExtras.jl#26 for a standard format across the ecosystem

Just like LGFlows.jl, JuMP can be removed as a dependency from the package by explicitly building the LP problem and solving it using MathProgBase.jl

A maximum_matching or more precise maximum_cardinality_matching function can be useful. This will add no new dependences.
Will work on this as well so feel free to assign this issue to me ;)