My first attempt at trying to get the links from groups page.

gistfile1.rb

require 'rubygems'
require 'mechanize'
require 'pry'

agent = Mechanize.new
page = agent.get('http://www.facebook.com/ed.drain')
page = agent.page.link_with(:href => 'https://www.facebook.com/bookmarks/groups#').click
agent.page.link_with(:href => 'https://www.facebook.com/bookmarks/groups')
page.links.each do |link|
  puts link.text
end