Has anyone seen a 4x4 graduation hat/mortar board applique? Thank you.

Have a look on embroiderydesigns.com I just had a look and they've got dozens. Didn't check on the size but you can do that quite easily by clicking on the design of your choice. I typed the word Graduation, into the little search box on the web site so that it narrows the search for you.

Thank you ladies. You are so awesome.

There is a nice one on Sewforum - link below, love and blessings Chris

The only one that I was able to find when I was doing graduation gifts recently was an applique version from BlastOStitch. Each of their designs comes in a range of sizes. I believe the filled version is available too, but I happened to be lucky enough to get the daily freebie.
There are a few in SewForum too, but they have names and such that you will have to delete unless you get lucky.