Graphs.jl is a good package for constructing graphs. You can build them in various ways, by adding vertices and edges, from matrices, etc.
For drawing graphs, there are a number of packages that display graphs made with Graphs.jl:
- TikzGraphs.jl: backend: Tikz/Latex
- GraphPlot.jl: backend: Compose.jl
- SGtSNEpi.jl: backend: Makie.jl
- GraphRecipes.jl: backend: Plots.jl
- GraphMakie.jl: backend: Makie.jl
- Karnak.jl: backend: Luxor.jl