In the analysis of social networks many relatively loose and heuristic definitions of 'community' abound. In this paper the concept of closely knit communities is studied as defined by the property that every pair of its members are neighbors or has at least one common neighbor, where the neighboring relationship is based on some more or less durable and stable acquaintance or contact relation. In this paper these are studied in the form of graphs or networks of diameter two (2-clubs). Their structure can be characterized by investigating shortest spanning trees and girth leading to a typology containing just three or, in combination, six types of close communities.