This is an extremely important part of our human nature. This is best identified with biblical word koinonia, which means "fellowship." God's plan from the beginning was that all of us would belong to a spiritual community where we would know others and be known.
Small groups are for personal and spiritual growth. They are designed to help people not only build relationships with each other, but also build or enhance their relationship with Christ. Your focus, then, is to spur that growth.
Outreach is also an important element of our purpose. An outward focus does not diminish the atmosphere of care and support in a group—it increases it. And a strong outward focus is also incomplete in and of itself. Groups that focus on reaching others for Christ must also nurture caring relationships in order to draw new people into the life of their group.