@dharr 

Lovely solution ... than's for introducting me to DataFrame.

@Kitonum 

Thank you!

@Carl Love 

Thank you for your (usual!) speedy assistance. This is a great help.

Suppose the 4 points are labelled A,B,C and D (can we assign a name to each point?)

Then I would look for a 4x4 matrix with column labels, A, B, C and D and also row labels A, B, C and D and at each intersection, the distance would be recorded. Ideally, I would love to export the results to Excel - please see attached Excel sheet.

Mapleprimes.xlsx

@Carl Love 

This is very useful and insightful. I thank you!

@Thomas Richard

Thanks for this ... interesting.

@Lenin Araujo Castillo 

The Maple routine is quite useful - thanks so much.

Suppose a relation under investigation is nonlinear. Do you know how this is treated?

@Carl Love 

Very interesting ... this worked just fine and satisfied a little curiosity!

Thanks (again!).

@tomleslie 

This is a welcomed addition to the solution ... I'm obliged!

@tomleslie 

As usual, you have provided a good insight intyo this problem .... I thank you for that.

The classification routine is great and on the matter of a non-source/sink, I'll explore this further. The matrices, A and B, were for the sake of example only - I'll run some more representative problems to test this out.

Thanks again!

@Kitonum 

This seems to have done the job - thank you so much!

I like your routine ... with this, I can move on.

Thanks again.

@Kitonum 

Yes - I can relabel the vertices as you proposed. The Help link was very useful ... thanks.

However, I might be on the wrong track here. I wish to assign labels (letters) to the matrix rows and numbers to the matrix columns as mentioned in the problem statement. The sources lie in the row number; the sinks lie in the columns that have entries=1. 

@Kitonum 

Thank you for the suggestion - much appreciated.

However, I tried to apply this to the matrix B graph ... I can't seem to find a way to replicate your method.

@tomleslie 

These are very useful insights you provided - I appreciate you taking the time and effort to share these. 

And of course, you are completely right -  the worksheet source file should have been attached rather than the pdf. I'll remember that in future also!

Thanks again...

@Carl Love 

It is great to get this workaround - thank you! It makes life so much easier ... now I can visualise the relationships of the solutions.

Thanks (again!) for your generous support.

Thank you, Carl. 

I tried that - but doesn't the adjacency matrix has 2 non-zero diagonal entries? If so - then the routine won't run.

Perhaps I am misinterpreting your suggestion (I am new to Graph Theory) - in this instance, the solution to my LP problem is given by the square matrix,Y, and will change as certain conditions / values are altered in the model. In other words, the entries will vary on a case-by-case basis and I simply wish to show these on a graph.