Formula for the number of connections needed to connect every node in a set?












6












$begingroup$


Assuming you have a set of nodes, how do you determine how many connections are needed to connect every node to every other node in the set?



Example input and output:



In   Out
<=1 0
2 1
3 3
4 6
5 10
6 15









share|cite|improve this question











$endgroup$

















    6












    $begingroup$


    Assuming you have a set of nodes, how do you determine how many connections are needed to connect every node to every other node in the set?



    Example input and output:



    In   Out
    <=1 0
    2 1
    3 3
    4 6
    5 10
    6 15









    share|cite|improve this question











    $endgroup$















      6












      6








      6


      1



      $begingroup$


      Assuming you have a set of nodes, how do you determine how many connections are needed to connect every node to every other node in the set?



      Example input and output:



      In   Out
      <=1 0
      2 1
      3 3
      4 6
      5 10
      6 15









      share|cite|improve this question











      $endgroup$




      Assuming you have a set of nodes, how do you determine how many connections are needed to connect every node to every other node in the set?



      Example input and output:



      In   Out
      <=1 0
      2 1
      3 3
      4 6
      5 10
      6 15






      combinatorics graph-theory






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      share|cite|improve this question













      share|cite|improve this question




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      edited Jan 1 '12 at 3:46









      J. M. is not a mathematician

      61.1k5151290




      61.1k5151290










      asked Jul 18 '11 at 16:32









      Jake PetroulesJake Petroules

      17617




      17617






















          3 Answers
          3






          active

          oldest

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          8












          $begingroup$

          If there are $n$ nodes, then this is called "$n$ choose $2$", and is equal to the number of $2$-element subsets of a set of $n$ elements. The Wikipedia article on binomial coefficients includes this and generalizations.



          Since I started writing you discovered the correct formula. However, if you ever have a similar problem where you are trying to figure out a general form for the terms in a sequence from some initial values, a good tool is The On-Line Encyclopedia of Integer Sequences. In this case, entering 0,1,3,6,10,15 brings up a useful entry in which you can find the general form and references.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!
            $endgroup$
            – Jake Petroules
            Jul 18 '11 at 17:55



















          6












          $begingroup$

          Here is what you want.$$sum_{k=1}^{n-1}k=frac{n(n-1)}{2}$$






          share|cite|improve this answer









          $endgroup$





















            2












            $begingroup$

            Figured it out. The formula is:



            x = n(n - 1) / 2





            share|cite|improve this answer









            $endgroup$













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              3 Answers
              3






              active

              oldest

              votes








              3 Answers
              3






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              8












              $begingroup$

              If there are $n$ nodes, then this is called "$n$ choose $2$", and is equal to the number of $2$-element subsets of a set of $n$ elements. The Wikipedia article on binomial coefficients includes this and generalizations.



              Since I started writing you discovered the correct formula. However, if you ever have a similar problem where you are trying to figure out a general form for the terms in a sequence from some initial values, a good tool is The On-Line Encyclopedia of Integer Sequences. In this case, entering 0,1,3,6,10,15 brings up a useful entry in which you can find the general form and references.






              share|cite|improve this answer









              $endgroup$













              • $begingroup$
                That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!
                $endgroup$
                – Jake Petroules
                Jul 18 '11 at 17:55
















              8












              $begingroup$

              If there are $n$ nodes, then this is called "$n$ choose $2$", and is equal to the number of $2$-element subsets of a set of $n$ elements. The Wikipedia article on binomial coefficients includes this and generalizations.



              Since I started writing you discovered the correct formula. However, if you ever have a similar problem where you are trying to figure out a general form for the terms in a sequence from some initial values, a good tool is The On-Line Encyclopedia of Integer Sequences. In this case, entering 0,1,3,6,10,15 brings up a useful entry in which you can find the general form and references.






              share|cite|improve this answer









              $endgroup$













              • $begingroup$
                That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!
                $endgroup$
                – Jake Petroules
                Jul 18 '11 at 17:55














              8












              8








              8





              $begingroup$

              If there are $n$ nodes, then this is called "$n$ choose $2$", and is equal to the number of $2$-element subsets of a set of $n$ elements. The Wikipedia article on binomial coefficients includes this and generalizations.



              Since I started writing you discovered the correct formula. However, if you ever have a similar problem where you are trying to figure out a general form for the terms in a sequence from some initial values, a good tool is The On-Line Encyclopedia of Integer Sequences. In this case, entering 0,1,3,6,10,15 brings up a useful entry in which you can find the general form and references.






              share|cite|improve this answer









              $endgroup$



              If there are $n$ nodes, then this is called "$n$ choose $2$", and is equal to the number of $2$-element subsets of a set of $n$ elements. The Wikipedia article on binomial coefficients includes this and generalizations.



              Since I started writing you discovered the correct formula. However, if you ever have a similar problem where you are trying to figure out a general form for the terms in a sequence from some initial values, a good tool is The On-Line Encyclopedia of Integer Sequences. In this case, entering 0,1,3,6,10,15 brings up a useful entry in which you can find the general form and references.







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered Jul 18 '11 at 16:46









              Jonas MeyerJonas Meyer

              40.6k6146254




              40.6k6146254












              • $begingroup$
                That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!
                $endgroup$
                – Jake Petroules
                Jul 18 '11 at 17:55


















              • $begingroup$
                That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!
                $endgroup$
                – Jake Petroules
                Jul 18 '11 at 17:55
















              $begingroup$
              That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!
              $endgroup$
              – Jake Petroules
              Jul 18 '11 at 17:55




              $begingroup$
              That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!
              $endgroup$
              – Jake Petroules
              Jul 18 '11 at 17:55











              6












              $begingroup$

              Here is what you want.$$sum_{k=1}^{n-1}k=frac{n(n-1)}{2}$$






              share|cite|improve this answer









              $endgroup$


















                6












                $begingroup$

                Here is what you want.$$sum_{k=1}^{n-1}k=frac{n(n-1)}{2}$$






                share|cite|improve this answer









                $endgroup$
















                  6












                  6








                  6





                  $begingroup$

                  Here is what you want.$$sum_{k=1}^{n-1}k=frac{n(n-1)}{2}$$






                  share|cite|improve this answer









                  $endgroup$



                  Here is what you want.$$sum_{k=1}^{n-1}k=frac{n(n-1)}{2}$$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Jul 18 '11 at 16:45









                  XiangXiang

                  478313




                  478313























                      2












                      $begingroup$

                      Figured it out. The formula is:



                      x = n(n - 1) / 2





                      share|cite|improve this answer









                      $endgroup$


















                        2












                        $begingroup$

                        Figured it out. The formula is:



                        x = n(n - 1) / 2





                        share|cite|improve this answer









                        $endgroup$
















                          2












                          2








                          2





                          $begingroup$

                          Figured it out. The formula is:



                          x = n(n - 1) / 2





                          share|cite|improve this answer









                          $endgroup$



                          Figured it out. The formula is:



                          x = n(n - 1) / 2






                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered Jul 18 '11 at 16:40









                          Jake PetroulesJake Petroules

                          17617




                          17617






























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