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Do not confuse the DR with an OSPF router type.
A given physical router can have some interfaces that are designated ( DR ), others that are backup designated ( BDR ), and others that are non-designated.
If no router is DR or BDR on a given subnet, the DR is first elected, and then a second election is held if there is more than one BDR.
( A DR Election Detail Simulation shows a step-by-step DR election example: How neighbor list, neighbor state, DR, and BDR are changed when receiving Hello ) The DR is elected based on the following default criteria:

2.162 seconds.