Shortest Paths Between ALL Pairs of Nodes in a Connected Graph

largest node number <MM,     
 A[ ], B[ ] reduced to representing graph in short adjacency form  (remove all pairs A[K] < B[K])  
    Therefore, for any linked pair A[K] - B[K], (B[K] is a neighbor of A[K])
       0 < K <= Nlinks   (number of links)       and for every K,   A[K] > B[K]

For any K, let  I=A[K]  and J=B[K].   So  I > J.

The graph must have less than M nodes.
Let M - 1 be the largest allowed integer-label on any node in the graph:

   0 < J  < I  < M

    J <= I - 1,      I <= M - 1
   
  J <= (M - 1) - 1

  J <= M - 2

  
 M*J  +  I  will be an index in an array C[NN]
 To make C[ ] long enough to contain all values of  M*J + I, for  0 < J < I < M.

 M*J  +  I  <= M*(I - 1) + I  <= M*I  -  M  + I  <= M*(M - 1)  -  M  + 1  =  M*M  - 2M  + 1  =  
                  = (M - 1)^2  < (M - 1)^2  + 1  = M^2  -  2*M  + 2 = NN
               
 if M=100 then NN = 10000  - 200  +  2   =  9202
 if M=50  then NN =  2500   -  100  +  2  =   2402

 If the largest integer-label is less than 100, 
      then the array C[  ] should have a length of 9202.  Declare C[NN] = C[9202].
 if 50, then declare C[NN] = C[2402].

                                    ***

 if H = M - 1 nodes,  H*(H - 1)/ 2  is the number of links in a complete graph.
  
  But  (M - 1)*(M - 2) / 2  =  [ M^2  -  3*M  + 2 ]/2   <  [M^2  - 2*M  + 2]/2   =  NN/2.

   So  in any graph with less than M nodes there are less than NN linked pairs.