Brief
I haven't fully tested the code so I can't be 100% sure it works, but, I ran it against a few different URLs and it seems to be working correctly.
I've taken parts of these answers:
Answer
Answer with domain names
This is what I've come up with:
(?(DEFINE)
  (?<scheme>[a-z][a-z0-9+.-]*)
  (?<userpass>([^:@\/](:[^:@\/])?@))
  (?<domain>[a-z0-9]+(-[a-z0-9]+)*(\.[a-z0-9]+(-[a-z0-9]+)*)+)
  (?<ip>(([0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,7}:|([0-9a-fA-F]{1,4}:){1,6}:[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,5}(:[0-9a-fA-F]{1,4}){1,2}|([0-9a-fA-F]{1,4}:){1,4}(:[0-9a-fA-F]{1,4}){1,3}|([0-9a-fA-F]{1,4}:){1,3}(:[0-9a-fA-F]{1,4}){1,4}|([0-9a-fA-F]{1,4}:){1,2}(:[0-9a-fA-F]{1,4}){1,5}|[0-9a-fA-F]{1,4}:((:[0-9a-fA-F]{1,4}){1,6})|:((:[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(:[0-9a-fA-F]{0,4}){0,4}%[0-9a-zA-Z]{1,}|::(ffff(:0{1,4}){0,1}:){0,1}((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])|([0-9a-fA-F]{1,4}:){1,4}:((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])))
  (?<host>((?&domain)|(?&ip)))
  (?<port>(:[\d]{1,5}))
  (?<path>([^?;\#]*))
  (?<query>(\?[^\#;]*))
  (?<anchor>(\#.*))
)
^(?:(?&scheme):\/\/)?(?&userpass)?(?<address>(?&host))(?&port)?\/?(?&path)?(?&query)?(?&anchor)?$
Follow this link to see it in use
Answer without domain names
The above regex will match URLs containing valid domains (whether it be a domain name or address). If you want to match only IP addresses, use the following regex (which includes a simple change in the definition group named host - I removed the reference to the definition group named domain)
(?(DEFINE)
  (?<scheme>[a-z][a-z0-9+.-]*)
  (?<userpass>([^:@\/](:[^:@\/])?@))
  (?<domain>[a-z0-9]+(-[a-z0-9]+)*(\.[a-z0-9]+(-[a-z0-9]+)*)+)
  (?<ip>(([0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,7}:|([0-9a-fA-F]{1,4}:){1,6}:[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,5}(:[0-9a-fA-F]{1,4}){1,2}|([0-9a-fA-F]{1,4}:){1,4}(:[0-9a-fA-F]{1,4}){1,3}|([0-9a-fA-F]{1,4}:){1,3}(:[0-9a-fA-F]{1,4}){1,4}|([0-9a-fA-F]{1,4}:){1,2}(:[0-9a-fA-F]{1,4}){1,5}|[0-9a-fA-F]{1,4}:((:[0-9a-fA-F]{1,4}){1,6})|:((:[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(:[0-9a-fA-F]{0,4}){0,4}%[0-9a-zA-Z]{1,}|::(ffff(:0{1,4}){0,1}:){0,1}((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])|([0-9a-fA-F]{1,4}:){1,4}:((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])))
  (?<host>(?&ip))
  (?<port>(:[\d]{1,5}))
  (?<path>([^?;\#]*))
  (?<query>(\?[^\#;]*))
  (?<anchor>(\#.*))
)
^(?:(?&scheme):\/\/)?(?&userpass)?(?<address>(?&host))(?&port)?\/?(?&path)?(?&query)?(?&anchor)?$
Follow this link to see it in use
For those who like a nice long non-legible query you can use the following regex which is equivalent to the one above.
^(?:[a-z][a-z0-9+.-]*:\/\/)?(?:[^:@\/](?::[^:@\/])?@)?(?<address>(?:[0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F]{1,4}|(?:[0-9a-fA-F]{1,4}:){1,7}:|(?:[0-9a-fA-F]{1,4}:){1,6}:[0-9a-fA-F]{1,4}|(?:[0-9a-fA-F]{1,4}:){1,5}(?::[0-9a-fA-F]{1,4}){1,2}|(?:[0-9a-fA-F]{1,4}:){1,4}(?::[0-9a-fA-F]{1,4}){1,3}|(?:[0-9a-fA-F]{1,4}:){1,3}(?::[0-9a-fA-F]{1,4}){1,4}|(?:[0-9a-fA-F]{1,4}:){1,2}(?::[0-9a-fA-F]{1,4}){1,5}|[0-9a-fA-F]{1,4}:(?:(?::[0-9a-fA-F]{1,4}){1,6})|:(?:(?::[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(?::[0-9a-fA-F]{0,4}){0,4}%[0-9a-zA-Z]{1,}|::(?:ffff(?::0{1,4}){0,1}:){0,1}(?:(?:25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9])\.){3,3}(?:25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9])|(?:[0-9a-fA-F]{1,4}:){1,4}:(?:(?:25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9])\.){3,3}(?:25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9]))(?::[\d]{1,5})?\/?(?:[^?;\#]*)?(?:\?[^\#;]*)?(?:\#.*)?$
Note: Both answers use the i (case insensitive) and x (ignore whitespace) modifiers