Question: Is there a maple function comparable to RelationGraph?

Recently, I tried to write a function to get the lexicographic product of two graphs.

In  graph theory the lexicographic product G ∙ H of graphs G and H is a graph such that
  • the vertex set of G ∙ H is the cartesian product V(G) × V(H); and
  • any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent with x in G or u = x and v is adjacent with y in H.

I'm trying to write this function as defined after making sure it doesn't exist in maple. I saw a similar post by mathematica stack.

There are many answers in the post, the most interesting to me is the following code, which follows the definition of lexicographic product. 

lexicographicProduct[g1_?UndirectedGraphQ, g2_?UndirectedGraphQ, opt : OptionsPattern[]] := 
   (* two nodes are connected if their corresponding nodes in the first graph are connected *)
   EdgeQ[g1, First[#1] \[UndirectedEdge] First[#2]] || 
   (* or their corresponding nodes in the first graph are the same and their corresponding nodes in the second graph are connected *)
   (First[#1] === First[#2] && EdgeQ[g2, Last[#1] \[UndirectedEdge] Last[#2]]) &,

   (* the vertices are the cartesian product of the two vertex sets *)
   Tuples[{VertexList[g1], VertexList[g2]}],

   (* also allow setting graph options *)

lexicographicProduct[CycleGraph[5], CycleGraph[3]]

It utilizes the  function RelationGraph in Mathematica. I feel that this function is generic in nature. So here I would ask maple if they had a similar function.

Function RelationGraph is to generate a graph based on data and a binary relation.

For example, using RelationGraph  I  can get easily  the kth power Gk of an graph G which is another graph that has the same set of vertices, but in which two vertices are adjacent when their distance in G is at most k.

Dis[g1_?UndirectedGraphQ, k_] := 
  GraphDistance[g1, #1, #2] <= k && GraphDistance[g1, #1, #2] != 0 &, 
Dis[PathGraph[Range[10]], 2]

If I use maple and do not use the built-in function GraphPower, I might deal with the following.

local choo,edge,vex,g;
 choo:= choose(vex, 2):
 g:= Graph(Vertices(G)):
 for edge in choo do 
     if Distance(G, edge[1], edge[2])<=k  then 
        AddEdge(g, convert(edge,set))
  end do:
 return g;
end proc:



I believe if the RelationGraph function can be  implemented in maple, the function lexicographicProduct would be easier to obtain.

Please Wait...