Important is related to Famous. Famous is the opposite of Personality. Personality is related to Mood. Mood is related to Happy. 
Alone is a synonym of Lonely. Lonely is related to Island. Island is related to Tropical. Tropical is related to Palm. 
Important <--RelatedTo--> Famous <--Antonym--> Personality <--RelatedTo--> Mood <--RelatedTo--> Happy 
Alone <--Synonym--> Lonely <--RelatedTo--> Island <--RelatedTo--> Tropical <--RelatedTo--> Palm 