according to hrothgar, why does beowulf owe allegiance to the danes

As it turns out Beowulf's dad (try to follow this) was Ecgtheow. Ecgtheow had killed someone from another tribe and ran off before any score was settled. Hrothgar settled the feud by paying money to the family of the man who had been killed thus Ecgtheow swore his allegiance to Hrothgar. So this means that Beowulf still owes him because Beowulf's father owed him.