Here is my github-users script for instance:

#!/usr/bin/env ruby

require 'octokit'

Octokit.configure do |c|
  c.login = '....'
  c.password = '...'
end

get = Octokit.org(ARGV.first).rels[:public_members].get
members = get.data
urls = members.map(&:url)

while members.size > 0
  next_url = get.rels[:next]
  next members = [] unless next_url
  get = next_url.get
  members = get.data
  urls << members.map(&:url)
end

puts urls

e.g. github-members stackexchange gives:

https://api.github.com/users/JasonPunyon
https://api.github.com/users/JonHMChan
https://api.github.com/users/NickCraver
https://api.github.com/users/NickLarsen
https://api.github.com/users/PeterGrace
https://api.github.com/users/bretcope
https://api.github.com/users/captncraig
https://api.github.com/users/df07
https://api.github.com/users/dixon
https://api.github.com/users/gdalgas
https://api.github.com/users/haneytron
https://api.github.com/users/jc4p
https://api.github.com/users/kevin-montrose
https://api.github.com/users/kirtithorat
https://api.github.com/users/kylebrandt
https://api.github.com/users/momow
https://api.github.com/users/ocoster-se
https://api.github.com/users/robertaarcoverde
https://api.github.com/users/rossipedia
https://api.github.com/users/shanemadden
https://api.github.com/users/sklivvz