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Mathematics Wolfram Language

[?] Create a path matrix using Mathematica?

Nehal Elshaboury

Posted 6 years ago

I have created a code that finds all possible paths from source node (1) to demand node (4), as per the attached file. I need to create a path matrix in which, number of rows is equivalent to the number of paths, and number of columns is equivalent to the number of edges in a network. This matrix is a zero-one matrix with 1 as its (i, j)th entry if the edge is present in the path to the demand node, and 0 as its (i, j)th entry if it is not. For example, the first possible path to get from node (1) to node (4) is {a,e,f}. The corresponding matrix shall be {1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} and the same procedure goes for the other paths. The final path matrix shall be as the attached image Attachments: Trial-Path Matrix.nb

POSTED BY: Nehal Elshaboury

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Rohit Namjoshi

Posted 6 years ago

Nehal, One (not very computationally efficient) way to do this paths = {{a, e, f}, {a, b, c}, {a, i, l, j, f}, {a, e, h, g, d}, {a, i, m, q, o, j, f}, {a, i, l, n, k, h, f}, {a, i, l, n, k, g, d}, {a, i, l, j, h, g, d}, {a, e, j, n, k, g, d}, {a, i, m, r, u, t, o, j, f}, {a, i, m, r, u, p, n, j, f}, {a, i, m, r, u, p, k, h, f}, {a, i, m, r, u, p, k, g, d}, {a, i, m, q, t, p, n, j, f}, {a, i, m, q, t, p, k, h, f}, {a, i, m, q, t, p, k, g, d}, {a, i, m, q, o, n, k, h, f}, {a, i, m, q, o, n, k, g, d}, {a, i, m, q, o, j, h, g, d}, {a, i, l, o, t, p, k, h, f}, {a, i, l, o, t, p, k, g, d}, {a, e, j, o, t, p, k, g, d}, {a, i, m, s, v, u, t, o, j, f}, {a, i, m, s, v, u, p, n, j, f}, {a, i, m, s, v, u, p, k, h, f}, {a, i, m, s, v, u, p, k, g, d}, {a, i, m, r, u, t, o, n, k, h, f}, {a, i, m, r, u, t, o, n, k, g, d}, {a, i, m, r, u, t, o, j, h, g, d}, {a, i, m, r, u, p, n, j, h, g, d}, {a, i, m, q, t, p, n, j, h, g, d}, {a, i, l, o, q, r, u, p, k, h, f}, {a, i, l, o, q, r, u, p, k, g, d}, {a, e, j, o, q, r, u, p, k, g, d}, {a, e, j, l, m, r, u, p, k, g, d}, {a, e, j, l, m, q, t, p, k, g, d}, {a, i, m, s, v, u, t, o, n, k, h, f}, {a, i, m, s, v, u, t, o, n, k, g, d}, {a, i, m, s, v, u, t, o, j, h, g, d}, {a, i, m, s, v, u, p, n, j, h, g, d}, {a, i, l, o, q, s, v, u, p, k, h, f}, {a, i, l, o, q, s, v, u, p, k, g, d}, {a, e, j, o, q, s, v, u, p, k, g, d}, {a, e, j, l, m, s, v, u, p, k, g, d}} nodeLabels = paths // Flatten // Union; nodeCount = nodeLabels // Length; indexes = Map[ToString /* LetterNumber, paths, {-1}]; matrix = Map[SparseArray[# -> ConstantArray[1, Length@#]] & /* Normal /* (PadRight[#, nodeCount] &), indexes]; Grid[matrix // Prepend[nodeLabels], Frame -> All, Background -> {Automatic, {1 -> Yellow}}]

Nehal,

One (not very computationally efficient) way to do this

paths = {{a, e, f}, {a, b, c}, {a, i, l, j, f}, {a, e, h, g, d}, {a, 
   i, m, q, o, j, f}, {a, i, l, n, k, h, f}, {a, i, l, n, k, g, 
   d}, {a, i, l, j, h, g, d}, {a, e, j, n, k, g, d}, {a, i, m, r, u, 
   t, o, j, f}, {a, i, m, r, u, p, n, j, f}, {a, i, m, r, u, p, k, h, 
   f}, {a, i, m, r, u, p, k, g, d}, {a, i, m, q, t, p, n, j, f}, {a, 
   i, m, q, t, p, k, h, f}, {a, i, m, q, t, p, k, g, d}, {a, i, m, q, 
   o, n, k, h, f}, {a, i, m, q, o, n, k, g, d}, {a, i, m, q, o, j, h, 
   g, d}, {a, i, l, o, t, p, k, h, f}, {a, i, l, o, t, p, k, g, 
   d}, {a, e, j, o, t, p, k, g, d}, {a, i, m, s, v, u, t, o, j, 
   f}, {a, i, m, s, v, u, p, n, j, f}, {a, i, m, s, v, u, p, k, h, 
   f}, {a, i, m, s, v, u, p, k, g, d}, {a, i, m, r, u, t, o, n, k, h, 
   f}, {a, i, m, r, u, t, o, n, k, g, d}, {a, i, m, r, u, t, o, j, h, 
   g, d}, {a, i, m, r, u, p, n, j, h, g, d}, {a, i, m, q, t, p, n, j, 
   h, g, d}, {a, i, l, o, q, r, u, p, k, h, f}, {a, i, l, o, q, r, u, 
   p, k, g, d}, {a, e, j, o, q, r, u, p, k, g, d}, {a, e, j, l, m, r, 
   u, p, k, g, d}, {a, e, j, l, m, q, t, p, k, g, d}, {a, i, m, s, v, 
   u, t, o, n, k, h, f}, {a, i, m, s, v, u, t, o, n, k, g, d}, {a, i, 
   m, s, v, u, t, o, j, h, g, d}, {a, i, m, s, v, u, p, n, j, h, g, 
   d}, {a, i, l, o, q, s, v, u, p, k, h, f}, {a, i, l, o, q, s, v, u, 
   p, k, g, d}, {a, e, j, o, q, s, v, u, p, k, g, d}, {a, e, j, l, m, 
   s, v, u, p, k, g, d}}

nodeLabels = paths // Flatten // Union;
nodeCount = nodeLabels // Length;

indexes = Map[ToString /* LetterNumber, paths, {-1}];
matrix = Map[SparseArray[# -> ConstantArray[1, Length@#]] & /* Normal /* (PadRight[#, nodeCount] &), indexes];

Grid[matrix // Prepend[nodeLabels], Frame -> All, Background -> {Automatic, {1 -> Yellow}}]

enter image description here

POSTED BY: Rohit Namjoshi

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