no matter how your situation is after graduation, (e.g. you get a temporary employment, you continues studie or do other things) we always recommend to have your status in the A-kasse changed to/registered as "graduate". This way you can use your "graduate rights" up to two years after graduation, meaning that you can get unemployment benefits ("dagpenge") without needing to fullfill the normal requirements for being eligible for getting unemployment benefits.
You can also receive dagpenge for the periods you dont work. So if you have a gig for 1 week about 1 month after graduation, then you can receive full dagpenge for the first month after graduation, and for the month where you have the gig, you can also get dagpenge, BUT for 1 week less. You are obliged to inform your A-kasse about temporary jobs - like freelancer job - when you receive dagpenge. You do this on the monthly benefit-card ("dagpengekort") that you fill out online on your A-kasse's website ones every month.
If you have not earned income by working during your studies, you will not be able to obtain right to unemployment benefits ("Dagpenge") the normal way, therefor you only have the option to use the graduate rule.
So we strongly recommend you to get your status changed (from student) to "graduated" in your A-kasse AT LATEST 14 DAYS AFTER GRADUATION.
If you wait until 2 months after, you will loose the possibility to have graduate rights, and also you will not receive dagpenge for the time up to your first gig.
You are entitled to get dagpenge - so why not get it? There is no reason why you should wait to get dagpenge until after your first gig. And if you wait you can propably not get any dagpenge at all, because you have not had normal/enough income during your study.
As from 1. of july 2017 you also now get extra benefits by working during a period where you receive dagpenge. Every time you have 1 hour of work you get two hours extra dagpenge in the last end (when your 2 years/3.848 hours dagpenge period is expired). And at the same you spend less of your benefit/dagpenge hours.
So take all the gigs you can have - it is an advantage in several ways for you.
And if you use the graduate rule, and get jobs after graduation there is also an extra benefit:
If you are a graduate and receive the benefit rate ("dagpengesats") for graduates, you can have your "dagpengesats" recalculated after you have had at least 3 months of work and income after you finish study.
If you are full-time insured, you need to work for a minimum of 320 hours before you can get the normal benefit rate ("dagpengesats").
If you have a monthly salary of at least DKK 22,230 (2017) you can get the highest "dagpengesats". As a graduate you only receive 71,5% (82% if you have dependent children).
Be aware that you can not require this recalculation before after 6 months.
Hope this helps you.
Please comment on this if you need further information.