Building a distance matrix

Question

I came across an interesting exercise that I would like to try to solve with Mathematica to improve my skills. In data is provided to build a distance matrix. The data looks like this, starting from node0 to node99:

node0, node1 0.04, node8 11.11, node14 72.21
node1, node46 1247.25, node6 20.59, node13 64.94
node2, node66 54.18, node31 166.80, node45 1561.45
node3, node20 133.65, node6 2.06, node11 42.43

I was just wondering how would you start doing this. I imported the file using Import["file.txt", "Data"]. I've been trying to make strings of each line and to drop the 1st element of the string, but I can't seem to get this. I started by doing:

number_nodes=100
max_node=99
data= Import["file.txt", "Data"]

Currently stuck at this stage Any help would be greatly appreciated :)

Answer 1

Note that there may be some mistakes in this solution, but it should give you a general idea and you can fix mistakes if you find any. Here is how I did it: I downloaded and saved the file as "temp.txt" in my working directory. Then I read the file and remove the first line:

graph = ReadList["temp.txt", String]
graph = Rest[graph];

Then I extracted the distances by cleaning up the text and splitting at spaces or commas:

dists = Table[
  Cases[ToExpression[StringSplit[graph[[i]], Whitespace | "," ]], _?
    NumericQ], {i, Length@graph}]

Then I got the connectivity by first finding all the instances of "node", made them numbers using `ToExpression' and added 1 to adjust from zero based arrays in Python:

nodeslist = 
 ToExpression@
   Table[StringCases[graph[[i]], 
     "node" ~~ x : RegularExpression["\\d+"] -> x], {i, 
     Length@graph}] + 1

The first instance of node in each of these is basically the node number, therefore it is easier to remove it. Also, some nodes like the last one (node99 in the original file) are not connected to any other nodes and are empty. So I removed them:

connectivity = Rest /@ nodeslist /. {} -> Nothing

Then I created assignment rules and created a sparse array:

arrayrules = 
  Table[{i, connectivity[[i, j]]} -> dists[[i, j]], {j, 1, 
    Length@connectivity[[i]]}, {i, n - 1}];

mat=SparseArray[arrayrules[[1]], {100, 100}]

You can convert back to a normal matrix using Normal and visualize it:

mat// Normal // MatrixForm

Also using MatrixPlot:

Answer 2

M = Array[m, {100, 100}]; (*the matrix; placeholder for its entries;*)
list = Import["graph.txt", "CSV"]; (*import the source data*)
graph = ToExpression[StringSplit[#] & /@ list]; (*reformat list to mathematica-friendly*)
node = Table[ToExpression["node" <> ToString[i]], {i, 0, 99}]; (*node variable naming*)
igraph = graph /. MapThread[(#1 -> #2) &, {node, Range[1, 100]}]; (*node variable indexification*)

(*igraph to graph-friendly structure; {i,j,m[i,j]}, m[i,j] is the dist btwn i & j*)
dist = Select[Flatten[Module[{x},
    x = #;
    Join[x[[1]], #] & /@ x[[2 ;; -1]]
] & /@ igraph, 1], Length@# > 1 &];

(*assign dist to the pairs*)
MapThread[(#1 = #2) &, {Map[Extract[M, #] &, dist[[All, 1 ;; 2]]], dist[[All, 3]]}];
(*assign string "." to the pairs without value*)
Map[If[Not[NumberQ[#]], # = "."] &, Flatten@M];

(*output first 10x10 of M*)
MatrixForm@M[[1 ;; 10, 1 ;; 10]]

If you expect the graph to be undirected, use the following dist instead:

dist = Flatten[Select[Flatten[Module[{x},
        x = #;
        Join[x[[1]], #] & /@ x[[2 ;; -1]]
    ] & /@ igraph, 1], Length@# > 1 &] /. {i_, j_, v_} -> {{i, j, v}, {j, i, v}}, 1];

--

Please feel free to take a look inside and play with the code. Note that though, if you execute the value assigning lines (MapThread) again after once it's executed, it will cause error because once you assign, it gets protected. In such case, clear the definitions.