#!/usr/bin/perl
$damp = 0.85;
$a = $b = $c = $d = $e = 0;
$f = 1; # We'll give the external site an "average" pagerank
$iterate = 40; # loop 40 times
# Extensive Interlinking - "Fully Meshed"
# forward links
# a -> b,c,d - 3 outgoing links - home
# b -> c,d,a - 3 outgoing links - about
# c -> d,a,b,e - 4 outgoing links - products
# d -> a,b,c - 3 outgoing links - more info
# e - nothing - site B
# f -> a - 1 outgoing link - exclusive link!
# i.e. "backward" links (what's pointing to me?)
# a <= b/3,c/4,d/3,f
# b <= c/4,d/3,a/3
# c <= d/3,a/3,b/3
# d <= a/3,b/3,c/3
# e <= c/4
# f <= we're going to assume it has enough incoming links to maintain a PR of 1.
while ($iterate--) {
printf("a: %.5f b: %.5f c: %.5f d: %.5f e: %.5f f: %.5f\n", $a, $b, $c, $d, $e, $f);
$a = 1 - $damp + $damp * ($b/3 + $c/4 + $d/3 + $f);
$b = 1 - $damp + $damp * ($c/4 + $d/3 + $a/3);
$c = 1 - $damp + $damp * ($d/3 + $a/3 + $b/3);
$d = 1 - $damp + $damp * ($a/3 + $b/3 + $c/4);
$e = 1 - $damp + $damp * ($c/4);
$f = 1; # this site has average SEO
}
Outputs
a: 0.00000 b: 0.00000 c: 0.00000 d: 0.00000 e: 0.00000 f: 1.00000
a: 1.00000 b: 0.43333 c: 0.55611 d: 0.67428 e: 0.26817 f: 1.00000
a: 1.43200 b: 0.86495 c: 0.99185 d: 1.01157 e: 0.36077 f: 1.00000
a: 1.74245 b: 1.14107 c: 1.25361 d: 1.23339 e: 0.41639 f: 1.00000
a: 1.93916 b: 1.31528 c: 1.42155 d: 1.37417 e: 0.45208 f: 1.00000
a: 2.06409 b: 1.42625 c: 1.52828 d: 1.46369 e: 0.47476 f: 1.00000
a: 2.14358 b: 1.49682 c: 1.59616 d: 1.52063 e: 0.48918 f: 1.00000
a: 2.19413 b: 1.54170 c: 1.63933 d: 1.55684 e: 0.49836 f: 1.00000
a: 2.22628 b: 1.57024 c: 1.66678 d: 1.57987 e: 0.50419 f: 1.00000
a: 2.24672 b: 1.58839 c: 1.68425 d: 1.59452 e: 0.50790 f: 1.00000
a: 2.25973 b: 1.59994 c: 1.69535 d: 1.60383 e: 0.51026 f: 1.00000
a: 2.26800 b: 1.60728 c: 1.70242 d: 1.60976 e: 0.51176 f: 1.00000
a: 2.27326 b: 1.61195 c: 1.70691 d: 1.61353 e: 0.51272 f: 1.00000
a: 2.27660 b: 1.61492 c: 1.70977 d: 1.61592 e: 0.51333 f: 1.00000
a: 2.27873 b: 1.61681 c: 1.71158 d: 1.61745 e: 0.51371 f: 1.00000
a: 2.28008 b: 1.61801 c: 1.71274 d: 1.61842 e: 0.51396 f: 1.00000
a: 2.28095 b: 1.61878 c: 1.71347 d: 1.61903 e: 0.51411 f: 1.00000
a: 2.28149 b: 1.61926 c: 1.71394 d: 1.61943 e: 0.51421 f: 1.00000
a: 2.28184 b: 1.61957 c: 1.71424 d: 1.61968 e: 0.51428 f: 1.00000
a: 2.28206 b: 1.61977 c: 1.71443 d: 1.61983 e: 0.51432 f: 1.00000
a: 2.28220 b: 1.61989 c: 1.71455 d: 1.61993 e: 0.51434 f: 1.00000
a: 2.28229 b: 1.61997 c: 1.71462 d: 1.62000 e: 0.51436 f: 1.00000
a: 2.28235 b: 1.62002 c: 1.71467 d: 1.62004 e: 0.51437 f: 1.00000
a: 2.28239 b: 1.62005 c: 1.71470 d: 1.62007 e: 0.51437 f: 1.00000
a: 2.28241 b: 1.62008 c: 1.71472 d: 1.62008 e: 0.51438 f: 1.00000
a: 2.28242 b: 1.62009 c: 1.71473 d: 1.62009 e: 0.51438 f: 1.00000
a: 2.28243 b: 1.62010 c: 1.71474 d: 1.62010 e: 0.51438 f: 1.00000
a: 2.28244 b: 1.62010 c: 1.71475 d: 1.62010 e: 0.51438 f: 1.00000
a: 2.28244 b: 1.62011 c: 1.71475 d: 1.62011 e: 0.51438 f: 1.00000
a: 2.28244 b: 1.62011 c: 1.71475 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71475 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000
a: 2.28245 b: 1.62011 c: 1.71476 d: 1.62011 e: 0.51439 f: 1.00000