Okay let's see.
TC = 2 to the power ((4x(3))/2) >> 2 p 6 = 2x2x2x2x2x2 = 64
logically, it checks out I think. Let's see. I said:
ie TC = (number of connection states) to the power (number of possible connection routes between nodes)
2 = connection states
node 4 = four outer connects
and on it's own - disregarding connections within the shape - follows the strict rule: (number of connection states) to the power (total number of nodes)
the inner is the bastard though. Basically - when you get to 4, that gives you 2 extra pathways - equalling 4 extra inner configurations for each of the outer configurations. Leaving us with:
((number of connection states) to the power (total number of nodes)) x (possible number of inner configurations)
ie. in the case of 4 nodes:
(2 power 4)x 4 = 64.
the hard bit though is the rule for possible inner config.
Okay, each extra node adds how many paths..?
4 nodes - 2 inner paths - and extra 2 for one increase in nodes.
5 nodes - 5 inner paths - an extra 3, for one increase in nodes.
6 nodes - 9 inner paths - an extra 4, for one increase in nodes.
Aha. Ze pattern forms. Kinda. Er.
hmm. Time for a fag.
Okay. I'm doing this the hard way. Inner/outer.
in a four node network - each node has 3 connections - but only the first node makes 3 new connections, the second (already connected to the first) makes 2 new connections, the third only 1, and the last 0.
ie 3+2+1+0 = 6 total.
Argh. okay. Google.Wiki answers
says - Where n = number of nodes
The number of connections in a full mesh = n(n - 1) / 2 (Way to go Anita!!! You are as clever as Wiki)
okay, so we had from earlier, from a three node:
TC = (number of connection states) to the power (total number of nodes)
But this is wrong. I fucked up at three because the number of nodes at that point equals the number of connections.
it should be:
(number of connection states) to the power (total number of connections
ie: 2 to the power n x (n - 1) / 2
node 1 - 2power1x0/2 = 0 config
node 2 - 2pwr2x1/2 = 2 config
nd3 - 2pwr3x2/2 = 8 config
nd4 - 2pwr4x3/2=64 config
nd5 - 2pwr5x4/2=2pwr10 config.
Tab, guesing wildly earlier, wrote:I'm guessing that for five nodes the total will be 2power 10 ie 2x2x2x2x2x2x2x2x2x2
Actually, looking back, I can't remember why I guessed this figure - but hey, I was right..! The important thing though, now I know why.
So, final rule:
The Maximum number of possible configurations within a network of N
nodes, where each connection has S
states - TC - is:TC = (S) to the power (n x (n - 1) / 2)
Great big thanks Anita
. You rock, and everybody else at ILP who didn't help, they suck.