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These are replies submitted by lcz

@vv  So, I want to aviod  this way Graphs_data:=[NonIsomorphicGraphs(4,restrictto =[connected], output = graphs, outputform =graph)]:  Since  the n=9  we already have 261080 graphs , but  
diameter 2 graphs are not many when n=9

@Joe Riel  These are really two different  questions,  In [1,1,2,2].   1 is  the second in my original intention. 

@mmcdara  I have realized your ideas. It is convenient to use your way test  for C4 or Kq. 

@vvthank you very much .It really helped me a lot

@tomleslie Thank you very much for the code you provided, which is exactly what I need. Maybe the algorithmIt's a little bit more complicated.

@Kitonum Thanks.  But it is a pity that  It doesn't solve my problem.
The difficult point is how to research the specific graph.

@sand15  What you said inspired me a lot. May be I should change  strategy .

@tomleslie  Thanks you first,  Just, in mathematica, I create it.  So I  hope Maple may improve it in the future.

@dharr I try it, and  make it. Thank you very much.

@sand15 I am very thanks to you for this act of kindness

@Carl Love thanks sir


 Dear Mr

CycleBasis returns a list of cycles in the graph, with each cycle represented as a list of vertices.  These cycles form a basis for the cycle space of G, so that every other cycle in G can be obtained from the cycle basis using only symmetric differences. (The symmetric difference is applied to cycles as sets of edges.)
• The elements of the basis are also known as fundamental cycles.
The number of elements in the cycle basis (i.e., the dimension of the cycle space) is called the cyclomatic number of G.

but the graph above ,we konw the number of cycles are more than 7. 

@mmcdara  thank you ! I mean cycles.   I will try  the order of cyclomatic number.

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