The JuliaGraphs ecosystem offers a set of abstractions and algorithms for various aspects of graph modeling and analysis. LightGraphs.jl is the central package defining the types and essential algorithms.

**Mentorship Inquiries**: Drop by #graphs on Slack or file a new issue on Github.

The LightGraphs.jl package provides a fast, robust set of graph analysis tools. This project would implement additions to LightGraphs to support parallel computation for a subset of graph algorithms. Examples of algorithms that would benefit from adaptation to parallelism would include centrality measures and traversals.

**Expected Results**: creation of LightGraphs-based data structures and algorithms that take advantage of large-scale parallel computing environments.

At the moment, LightGraphs.jl lacks algorithms that deal with graph planarity and familiar concepts. A candidate should study the literature and implement some algorithms that deal with planarity. Potential things that could be done:

- Implementation of tests for planarity and outer planarity
- Calculating a planar embedding of a graph
- There are some graph problems that have a much faster solution when a graph is planar.

GraphBLAS is a standard similar to BLAS for dealing with graphs. There also exists a reference implementation called SuiteSparse:GraphBLAS. It would be interesting to have a bridge from LightGraphs.jl to GraphBLAS, so we can compare the performance. A candidate should do the following:

- Get the GraphBLAS C API working from Julia and connect it to a GraphBLAS implementation.
- Implement the LightGraphs.jl interface using the GraphBLAS primitives.
- Overwrite LightGraphs methods with ones using GraphBLAS.
- Write benchmarks for comparing the GraphBlas and LightGraphs algorithms.

The GraphPlots.jl package could use some improvements:

- The current layout algorithms are fairly standard, there might be some newer improvements in the literature.
- There are layout algorithms for special graphs, such as directed acyclic graphs and trees.
- Some graph algorithms are embarrassingly parallel, we should make use of that.
- Make the interface easier to use; this could also simply mean improving the documentation.

LightGraphsMatching.jl currently depends on the external software BlossomV. In the past we had some problems calling that software from Julia and in addition it has a problematic license. Therefore it would be useful if we had a native Julia implementation of this algorithm. This is a rather advanced project. In addition to standard graph theory, a candidate should probably have some minor knowledge of linear programming and duality of linear programs.

LightGraphs.jl could use a set of benchmarks for measuring the performance of our algorithms and for spotting performance regressions in further updates. A candidate should do the following

- Create a set of benchmark algorithms that measure different aspects of LightGraphs.jl and cover different use cases.
- Find different graph classes for performing benchmarks, for example sparse/dense graphs and find some graphs that are a good approximation of the graphs that arise in typical datasets.
- Figure out how we could automatically run regression tests with these benchmarks when someone pushes a new PR to GitHub.