@lcz You wrote:

• Here I have not studied the corresponding relationship between graph vertex index and adjacency matrix index thoroughly. However,  it seems that Rows and columns of the adjacency matrix follow the order given by Vertices.

Yes, that is always true.
 

@dharr You wrote:

• I'm assuming the regular inverse is more efficiently calculated than the Moore-Penrose pseudoinverse.

When doing an exact computation, such as is being done here, the regular inverse is many times faster than the Moore-Penrose.

@bstuan You exclaimed:

• It's amazing how a seemingly complicated problem can be solved so simply!

This "textbook exercise" was highly contrived precisely to initially seem complicated yet have a simple solution. I'm a bit dubious of the pedagogy of that.

@ssgmckv You can't name a procedure 1/h0. You could name it h0 or `1/h0` (note the back quotes).

Technically, you are allowed to name a procedure D(D(F))(0), but I think it's a bad idea to do so. You could use DDF0 or `D(D(F))(0)`. Anything is a legal name if you put it in back quotes.

@bstuan See the comment that I just added to my Answer explaining how to do a "by hand" solution. And note that

exp(f(x)-x^2-1) = exp(f(x))*exp(-x^2-1) 

@ssgmckv If you want to do 3D contour plots of solutions of BVP system with the axes representing parameters and/or endpoint values (such as D(h)(0)), then see this Post: "Numerically solving BVPs that have many parameters"

@ssgmckv Please post a worksheet that shows the syntax error.

My knowledge of this area is quite superficial, so please excuse me if this question is trivial.

It seems to me that there are numerous pairs (x,y) from the set {e1, e2, e3, e4, e5, e6} for which your operation [x,y] hasn't been specified. For example, what are each of these: [e1,e2], [e2,e5], [e2,e6]? Is it sufficient to say that these are to be defined such that Jacobi's identity is satisfied? or perhaps that that is sufficient provided that it yields a unique definition?

If you create additional fake usernames to repost duplicates of this Question (as you just did), those usernames will just be blocked and the reposts deleted.

If you have something more to say about this Question, you're welcome to say it here (in this thread).

Stop posting duplicates of this Question.

You've given no indication whether or not you understand the Answer that I gave over a week ago.

FWIW, your ODE system is linear. I doubt that this makes much practical difference for solution attempts, but you may want to edit the Question's title.

@max125 Don't delete the earlier Question. Instead, either edit it or Reply to it. Either of those will put it at the top of the Active Conversations giving it renewed visibility.

@dharr Impressive solution technique; I vote up.

@Tokoro Sorry, I misinterpretted your Question, particularly the phrase "point to point", which I took to mean from a point to the next point going around the circle. Yes, I knew that not every pair of points in my construction had integer distance.

@Kitonum I like your solution! Here's a variation that's even shorter, and, better yet, removes the code's dependence on the length of x.

x:= <1 | 2 | 3 | 4>; #row vector
k:= <seq(x +~ a, a= x)>;

The OP should note that in this case the a iterates over the entries rather than the indices of x. 

@lcz Your for loops do nothing other than waste time repeating the same calculation (1830 times in this case). Your procedure can be simplified to

ResistanceMatrix:= (g::Graph)-> 
    (M-> Matrix(
            upperbound(M), (i,j)-> M[i,i]+M[j,j], 'shape' = 'symmetric'
         ) - 2*M
    )(LinearAlgebra:-MatrixInverse(
          GraphTheory:-LaplacianMatrix(g), 'method'= 'pseudo'
     ))
: