The best way is this:
- instead link type you can create a select type and fill DB parameter like screenshot (hidden on profile)
- for each select file you can create a delimeter field (visible only on profile) with this code in description:

<p><a href="/profile.html">Link to Family member</a></p>

This is possible wit our content plugin see docs at https://www.easy-profile.com/docs/26-plugin-content.html
- You can set condition on select field to hide delimeter if it is empty.
You can see an example of this on my test site. I will send you access via PM

Is this a feature that can be implemented at some point to show group/family relationships between users?

Yes but not for Easy Profile, we have developed a social network plugin to make Easy Profile like a social network. I see this as a feature for this plugin, I think something like circles for friendship.

Hi, sorry for my slow response! I finally have time to test this. I'm not sure I understand the steps to follow.

Should I first to this:
1. Create new field, Field Type = Delimeter

And then how do I create the link on a user's profile? Sorry for not understanding - I looked at the test site link you sent, but I didn't see the example. Thanks!

1. Create new field, Field Type = Delimeter

See screenshot

I looked at the test site link you sent, but I didn't see the example

Sorry try now, this is not official demo site, so is used by many users.