Nod is related to Sign. Sign is related to Hazard. Hazard is related to Threat. Threaten is derived from Threat. 
Authorize is the opposite of Prohibit. Prohibit is the opposite of Let. 
Nod <--RelatedTo--> Sign <--RelatedTo--> Hazard <--RelatedTo--> Threat <--DerivedFrom-- Threaten 
Authorize <--Antonym--> Prohibit <--Antonym--> Let 