Do you have a friend who is a similar size who might be able to loan you some clothes?
If the graduation is coming up soon, and in the U.K., you will probably want to wear a clean, smart coat, with a clean, smart scarf and polished warm shoes or boots. What you wear under your coat is unlikely to be seen very much so just wear something you like, and make sure it's clean and ironed, and any loose buttons sewn back on or trailing threads trimmed off.
Wear shoes or boots that are comfortable, as these events to involve a lot of standing around.
Make sure you turn off your mobile phone(s). Put a small bottle of water, a pack of tissues, and possibly a small snack (e.g. cereal bar) in your bag. Leave plenty of time to get there and plan your route (and parking, if you're driving) in advance, make sure you know which building, entrance, seat number, etc. and take any relevant paperwork.