Question

How do I make a Mathematica graph from edges with named vertices? EG:

http://pastebin.com/Se1Nhe3M

I’ve tried the above and several variations, but Combinatorica never
quite accepts it right. Apparently, Graph[] wants coordinate
positions, which I want Combinatorica to figure out itself.

AddVertex to EmptyGraph[0] (or whatever) also fails.

GraphUtilities isn’t an option, since I want to do fairly complex
analysis on my graphs.

This seems like a simple problem. Graphviz easily creates graphs from
edges with named vertices, so I’m sure Mathematica can too?

I’ve read:

ShowGraph[ { {e1,e2}, {e1, e3} }, {e1,e2,e3} ]; // what is the problem here?

but it doesn’t seem to help with my specific case.

Answer 1

If the sticking point is nodes represented as strings and the heavy-duty graph analysis functions want them as integers, you might consider mapping your strings to integers and vice versa:

nodes = DeleteDuplicates@Flatten[graph /. Rule -> List]

{"Conga", "Egypt", "Sarah Desert", "Europe", "Arabia", "UK", "Iceland", 
 "Greenland", "Germany", "Russia", "Irakistan", "Austr(al)ia", "China", "Canada",
 "More Russia", "USA", "Andy's Mountains", "Brazil"}

Now you have the list of nodes. Next do the mapping to and from integers:

each[{i_, s_}, Transpose[{Range@Length@nodes, nodes}],
  numify[s] = i;
  namify[i] = s]

You can now easily convert the nodes to and from integers:

numify["Europe"]

4

namify[4]

"Europe"

Convert the whole graph like this:

graph /. s_String -> numify[s]

Note that each is the following utility function, discussed here: ForEach loop in Mathematica

SetAttributes[each, HoldAll];               (* each[pattern, list, body]      *)
each[pat_, lst_, bod_] := ReleaseHold[      (*  converts pattern to body for  *)
  Hold[Cases[Evaluate@lst, pat:>bod];]];    (*   each element of list.        *)