@friends is just an instance variable that gets created then destroyed with every request.
Your best bet is to cache the response like so:
@friends = Rails.cache.fetch("friends-#{current_user.cache_key}") do
friends = FbGraph::User.me(current_user.oauth_token).friends
friends.map! do |friend|
friend if User.find_by_uid(friend.identifier) != nil
end
friends.compact!
end