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
- References:
- Integers networks
- From: Felice Russo <frusso@micron.com>
- Integers networks