interconnectedness and the duration of connections in several small networks¹

Abstract

introductionThe work described below is a preliminary test of one aspect of a social theory against some relevant empirical material. The approach adopts a limited view of society as networks of connections among biological points. Channels of connection may involve work, goods, information, or "pure" social exchanges.Network analysis has been used increasingly in the past decade (for reviews, see Mitchell 1969;Bott 1971;Whitten and Wolfe 1973) partly because it entails fewer cultural assumptions than does analysis in terms of specific groups like clans or classes. It is not only descriptively convenient but is also amenable to interesting mathematical manipulation. In addition to these methodological advantages, elementary laws of connection for networks of biosocial points, which are potentially of broad theoretical relevance, may be posited. The theory should be applicable to populations of any size, although it will require much more complex development for large populations than for the very small networks we have studied. We postulate that any connection that occurs between points in a social system sets up a field of attraction which alters the probability of occurrence of other connections. From this, in combination with certain other assumptions, a wide range of theoretical sociocultural propositions may be derived. Some of these are apparently testable; others are, for the time being, purely speculative.The argument can briefly be summarized as follows:The social realm may be conceived of in terms of points and connections among them.If a connection exists between X and Y, it will tend to continue and to increase in magnitude. If a connection also exists between Y and Z, as well as X and Y, there will be a tendency for the set to become interconnected by the establishment of a connection between X and Z. For any given set of conditions (involving terrain, technology, etc.) there are limitations on the number of a given kind o f connection that an individual, or set of individuals is capable of maintaining. The basic contradiction between the tendency to expand connections, combined with the limitations on the capacities for such expansion, may be resolved in several different ways. In the broad sense of the word, One aspect of a theory utilizing the concept of social network is examined empirically for five small networks, with an emphasis on hypothesized changes over time. An attempt is made to relate the distribution of the connections in these networks to their durations in terms of a measure of distance.networks 297

Assessing the role of social network interventions with an inner-city population.

“…Having a large second-order network is an important resource. Should the “friend of a friend” meet the client, the probability that they will become friends is high 16 . Thus, second-order contacts were occasionally tapped during periods of stress.…”

The Biometrics Research Unit of the New York State Department of Mental Hygiene

“…The Anthropology section, directed by Dr. Muriel Hammer, has pursued the development of techniques for specifying the structure of social networks-that is, the nature and degree of connectedness among individuals (Hammer et al, 1969;Hammer and Schaffer, 1975). In part, such work is an essential precursor of any attempt to follow up the earlier finding (Hammer, 1963-4), mentioned above, that patients' positions in their social networks appear to have important implications for the diagnosis and treatment of their psychopathology.…”