I assume you got a PD U2 document at the time of leaving Denmark for jobsearch up to 3 months.
In this PD U2 document it is also stated when the 3 months period expires.
If you do not find work, you must be back in Denmark, so you can sign up for your Jobcenter (Jobnet.dk) as unemployed before the end of the three-month period. This means that you must sign up for the Job Center in Denmark no later than the last day of the period stated in the PD U2 document. If you do not comply with this, you can not receive unemployment benefits in Denmark before you have worked for at least 296 hours within a period of 12 weeks.
It is not relevant to differ between if you were recent graduate or working when you left Denmark, because only people who are full unemployed before leaving Denmark and eligible for unemployment benefits, have the right to search for job with unemployment benefits, for up to 3 months in another EU/EEA country.
If you were eligible for unemployment benefits before you left Denmark, you will also be after returning to Denmark, provided that you meet the conditions mentioned above.