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Re: Integers networks
*To*: mathgroup at smc.vnet.net
*Subject*: [mg82318] Re: [mg82246] Integers networks
*From*: Fred Meinberg <fredm at wolfram.com>
*Date*: Wed, 17 Oct 2007 04:10:29 -0400 (EDT)
*References*: <200710160726.DAA08777@smc.vnet.net> <0E6AB70B-AD6A-4B41-A7EF-1DDEBC98D4ED@wolfram.com> <BF7367E20E0502458D0EF38851AD5FFD0720E06F@ntxavzmbx03.azit.micron.com>
Hi Felice,
The syntax is little compact, I agree.
The main function is FactorInteger, which returns the prime factors
of a number together with its exponents.
The [[All,1]] part returns only the first elements of the lists, that
is, the prime factors, not the exponents.
Thread[Rule[#,...]] makes sure that for each list of factor integers,
a list of rules is returned. For instance, 6 will go into {6->2, 6->3}.
Array is a function like Table but with a more compact syntax. So
Array[f, 2] gives {f[1], f[2]}, the same output as Table[f[i], {i,1,2}].
The Array expression returns a list of lists of rules. But for the
graph we want a flat list of rules connecting the nodes. So we use
the Flatten command.
I hope this helps.
-Fred-
On Oct 16, 2007, at 9:41 AM, <frusso at micron.com> wrote:
> Fred thanks
> It works. Please can you exaplin me better the following command?
> It is
> a function that for each number give the prime factor. But I didin't
> understand how it works.
>
> Flatten@Array[Thread[Rule[#, FactorInteger[#][[All, 1]]]] &, i]
>
> Thanks. Felice
>
>
> -----Original Message-----
> From: Fred Meinberg [mailto:fredm at wolfram.com]
> Sent: Tuesday, October 16, 2007 10:18 AM
> To: frusso
> Cc: mathgroup at smc.vnet.net
> Subject: Re: [mg82246] Integers networks
>
> try
>
> graph[i_] := Flatten@Array[Thread[Rule[#, FactorInteger[#][[All, 1]]]]
> &, i]
>
> a nice visualization is:
>
> Manipulate[GraphPlot[graph[i], SelfLoopStyle -> None], {i, 1, 100, 1}]
>
> On Oct 16, 2007, at 3:26 AM, Felice Russo wrote:
>
>> Hi
>> This is my first post in this forum.
>> I would like to generate a graph where each node is an integer number
>> and the edges the prime factors. For example the node 10 and
>> 2 will have an edge as also the nodes 10 and 5 being 2 and 5 the
>> prime
>
>> factors of 10.
>> And so on....
>> I know that I can generate the graph by using the adjacent matrix but
>> I think that there should be a more smart and easy method. Can you
>> help me?
>>
>> Thanks. Felice
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