My first try. Passes -w and strict. 172 characters. 
sub path {
my($g,$a,$b,$x,$y,%s)=@_;$s{$a}=[0,[$a]];for(%$g){for(keys%s){$s{$x}&&
+$s{$_}[0]+$y>$s{$x}[0]or$s{$x}=[$s{$_}[0]+$y,[@{$s{$_}[1]},$x]]while(
+$x,$y)=each%{$g->{$_}}}}$s{$b}[1]
}

[download]

Update:Oops, it returns an arrayref instead of an array. No point in fixing it, chipmunk's solution puts mine to shame anyway.

In reply to Re: (Golf) Shortest Graph Distance by no_slogan
in thread (Golf) Shortest Graph Distance by Masem

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.