While writing a wrapper to submit files for batch processing I found a need to find all the hard links to a file. Like so many things in Linux, the solution turns out to be simple -- once I found it.
Use the find command
$ find <dir to start search in> -xdev -samefile <path to file>
For example, to find all the hard link to the file /home/buser/chosen.one.txt on the home partition, use:
$ find /home -xdev -samefile /home/buser/chosen.one.txt
The switch -xdev means to only search on the original volume. It can be omitted but, because a hard link cannot cross volume boundaries, the switch will save time by not searching where a linked file cannot be anyways.