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How to generate a "triangular" graph for arbitrary given depth?

Matthias Drobnitzky
Posted 13 days ago

I am looking for a way to generate a "triangular" graph of the following shape for arbitrary given depth, with vertices at positions similar to the numbers in Pascal's triangle, and vertical edges only:

Graph[{1 -> 2, 1 -> 3, 2 -> 4, 2 -> 5, 3 -> 5, 3 -> 6, 4 -> 7, 4 -> 8,
   5 -> 8, 5 -> 9, 6 -> 9, 6 -> 10}, VertexLabels -> Automatic]

enter image description here

I was unsuccessful in using any of the parametric graphs available in Mathematica.

Thank you for any hints you might provide.
POSTED BY: Matthias Drobnitzky
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Eric Rimbey
Eric Rimbey
Posted 11 days ago

Another way:

With[
 {d = 5},
 Graph[
  Flatten[
   BlockMap[Inner[Rule, #[[1]], Partition[#[[2]], 2, 1], List] &, 
    TakeList[Range[d (d + 1)/2], Range[d]], 2, 1]],
  VertexLabels -> Automatic]]
POSTED BY: Eric Rimbey

Thank you, Eric. Your post contained commands (TakeList, Rule, BlockMap) that were new for me. I used your suggestion to construct a SparseArray whose AdjacencyMatrix is the requested graph.



				
					

						


































































	

		





































































	

	


	

	


					

				
				
			

				
	


	
	
		

			

				

					

































































				

				
    

					

					 

					
				

					
		

	

	

	
	
	
		

	
	
	
		
			

				
					
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Michael, thank you for the elegant solution that you had provided to my question.
It took me some time to digest, but I have learned a lot about postfix notation and pure function use.
Matthias


				
					

						


































































	

		





































































	

	


	

	


					

				
				
			

				
	


	
	
		

			

				

					

































































				

				
    

					

					 

					
				

					
		

	

	

	
	
	
		

	
	
	
		
			

				
					
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One way:


Block[{n = 6}, (* n >= 1 *)
  Flatten@Table[
    {Thread[DirectedEdge[
       k (k - 1)/2 // Range[1 + #, # + k] &,
       k (k + 1)/2 // Range[1 + #, # + k] &]
      ],
     Thread[DirectedEdge[
       k (k - 1)/2 // Range[1 + #, # + k] &,
       k (k + 1)/2 // Range[2 + #, # + k + 1] &]
      ]}, {k, n - 1}]
  ] // Graph[#, VertexLabels -> Automatic] &



				
					

						


































































	

		





































































	

	


	

	


					

				
				
			

				
	


	
	
		

			

				

					

































































				

				
    

					

					 

					
				

					
		

	

	

	
	
	
		

	
	
	
		
			

				
					
						POSTED BY: Michael Rogers
					
					
				
			

		
				
	
	
	
	

		
		
		

		

		

			

		
	


	

		

			

			
				
			
		
	


	










	       
	       
	



		




















































































	
	





	
		
			
			
				

				   

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