In our reply, we assume that you only ask for the opportunity to receive unemployment benefits ("Dagpenge") based on education (not work).
So for being eligible for "Dagpenge" as an graduate you must:
1. stay in Denmark the day before starting an (full) education of a duration of at least 18 months.
2. complete an education of at least 18 months/3 semester. This must be regarded as a full education, i.e. a bachelor, master or Top Up. The education does not have to be at a Danish educational institution. Also completed education from other countries will be ok, AS long as you meet the requirement for having address in Denmark prior to and again right after finishing education.
3. stay in Denmark again at latest 2 weeks after graduation.
4. Become member of an A-kasse at latest 2 weeks after graduation.
These requirements are the main requirements for graduates.
However as a non EU/EEA graduate you must take into account one more requirement.
For beeing eligble for Unemployment benefits ("Dagpenge") you must have residence and work permit. And the work permit must allow you to work FULL time in Denmark.
The 6 month job-search period included in a standard student permit, IS NOT sufficient, because this type of work permit only allows you to work up to 20 hours per month.
Thus, with a study permit you are not allowed to receive Unemployment benefits.
For being eligible for benefits you need work permit based on one of the others Schemes that gives you right to work full time.
Let us know if you have further questions or comments.