implementation of basic algebra for graphs

alga.fs

// https://blogs.ncl.ac.uk/andreymokhov/an-algebra-of-graphs/

type Vertex = string

type Graph(vertices:Set<Vertex>, edges:Set<(Vertex * Vertex)>) =
    member this.vertices = vertices
    member this.edges = edges

    member this.empty() = new Graph(Set.empty, Set.empty)
    member this.overlay(g:Graph) = new Graph(Set.union this.vertices g.vertices, Set.union this.edges g.edges)
    member this.connect(g:Graph) =
        let E = Set.union this.edges g.edges
        let EE = Set.map (fun x -> Set.map (fun y -> (x,y)) this.vertices) g.vertices 
                 |> Seq.concat 
                 |> Set.ofSeq
        new Graph(Set.union this.vertices g.vertices, Set.union E EE)
    static member (+) (g:Graph, this:Graph) = this.overlay g
    static member (*) (g:Graph, this:Graph) = this.connect g


let g1 = new Graph(set ["a"; "b"; "c"], set [("a", "b"); ("a", "c")])
let g2 = new Graph(set ["c";"d";"e"], set [("c","d"); ("d","e")])