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Re: Re: Finding paths in graphs

• To: mathgroup at smc.vnet.net
• Subject: [mg72550] Re: [mg72542] Re: Finding paths in graphs
• From: John Dickmann <jqd at mit.edu>
• Date: Sat, 6 Jan 2007 23:23:04 -0500 (EST)
• References: <enkrvm$9k0$1@smc.vnet.net> <200701060830.DAA02594@smc.vnet.net>

Arek,

this looks like it works (see addition in bold below).

john

>> << DiscreteMath`Combinatorica`
>> << DiscreteMath`GraphPlot`;
>> AllPaths[g_Graph, {a_, b_}] :=
>> Module[{s = {a}, done, npath = 0, e = ToAdjacencyLists[g], x,
>> v, ind, n = V[g], c = 0}, ind = Table[1, {n}];
>> While[Length[s] > 0, v = Last[s];
>> done = False;
>> While[ind[[v]] <= Length[e[[v]]] && !
>>         done, If[! MemberQ[s, (x = e[[v, ind[[v]]++]])], done =  
>> True]];
>>         If[done, s = {s, x}; s = Flatten[s]; If[(x ==
>>       b), Print[s]; npath = npath + 1;(*If[npath == c +
>>      1000, Print["npath:   ", npath]; c = npath];*)If[Length[s] >= 0,
>> s =
>>        Drop[s, -1]]],
>>           If[Length[s] > 0, s = Drop[s, -1]]; ind[[v]] =
>>              1]]; Print["Start node: ", a, "; End node: ", b, ";
>>          Number of Paths:  ", npath]]

On Jan 6, 2007, at 3:30 AM, Arkadiusz.Majka at gmail.com wrote:

> Great!
>
> John, could you please rewrite a bit your and Andrzej's code and print
> all pathes (not only their number)
>
> Thanks,
>
> Arek
>
>
> John Dickmann napisal(a):
>> OT,
>>
>> this works for me, courtesy of Andrezj Koslowski from a 1996 posting,
>> modified to improve speed some.
>>
>> If there's anybody else out there who has a faster way to do this,
>> I'd really like to see it.
>>
>> << DiscreteMath`Combinatorica`
>> << DiscreteMath`GraphPlot`;
>> AllPaths[g_Graph, {a_, b_}] :=
>> Module[{s = {a}, done, npath = 0, e = ToAdjacencyLists[g], x,
>> v, ind, n = V[g], c = 0}, ind = Table[1, {n}];
>> While[Length[s] > 0, v = Last[s];
>> done = False;
>> While[ind[[v]] <= Length[e[[v]]] && !
>>         done, If[! MemberQ[s, (x = e[[v, ind[[v]]++]])], done =  
>> True]];
>>         If[done, s = {s, x}; s = Flatten[s]; If[(x ==
>>       b), npath = npath + 1;(*If[npath == c +
>>      1000, Print["npath:   ", npath]; c = npath];*)If[Length[s] >= 0,
>> s =
>>        Drop[s, -1]]],
>>           If[Length[s] > 0, s = Drop[s, -1]]; ind[[v]] =
>>              1]]; Print["Start node: ", a, "; End node: ", b, ";
>>          Number of Paths:  ", npath]]
>>
>> john
>>
>> On Jan 4, 2007, at 7:00 AM, OT wrote:
>>
>>> Hi all,
>>>
>>> I have a big oriented graph in a Mathematica notebook, described  
>>> as a
>>> list of rule (i.e the graph is something like {1->2 , 1->3, 2-
>>>> 3, ... })
>>>   and I want to find all the path from vertex 'a' to vertex 'b'...
>>>
>>> How can I do that ? The function ShortestPath doesn't work on graphs
>>> defined in this way, and moreover this function only return one  
>>> of the
>>> shortest paths, while I'm looking for all the existing paths...
>>>
>>> thanks,
>>> OT
>>>
>>
>> John Q. Dickmann
>> Research Assistant
>> Lean Aerospace Initiative
>> Massachusetts Institute of Technology
>> Bldg 41-205
>> 77 Massachusetts Ave.
>> Cambridge, MA 02139
>>
>> jqd at mit.edu
>> 401-225-3511
>

John Q. Dickmann
Research Assistant
Lean Aerospace Initiative
Massachusetts Institute of Technology
Bldg 41-205
77 Massachusetts Ave.
Cambridge, MA 02139

jqd at mit.edu
401-225-3511

• References:
  • Re: Finding paths in graphs
    • From: Arkadiusz.Majka@gmail.com