Egg is related to Lay. Lay is a synonym of Ball. Ball can be used for Rolling. 
Common is similar to Frequent. Frequent is the opposite of Rare. Rare is related to Council. 
Egg <--RelatedTo--> Lay <--Synonym--> Ball --UsedFor--> Rolling 
Common <--SimilarTo--> Frequent <--Antonym--> Rare <--RelatedTo--> Council 