The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a 'functorial' mapping of the original pattern. Such a mapping

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... ly a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the 'theory of categories,' a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach. By interrelations among relations is meant the way in which relations among the members of a social system occur in characteristic bundles and how these bundles of relations interlock and determine one another. % By understanding is meant distilling simpler patterns at a higher level of abstraction-simpler not only in having fewer constituents but also in exhibiting interrelations which are more regular or transparent.