One of the meanings of "нет" is 'absence of smtn.': Никого для меня нет дороже... unlike English, Russian widely uses double negations. Verbatim translation of the phrase would be: "nobody is not dearer to me'.
У меня нет денег = I have no money
The particle "не" doesn't bear this meaning. It's normally placed right in front of the words it modifies (negates) :
Не сегодня = not today
Не очень много = not very much
Не знаю = (I) don't know