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History One the of the earliest writers to discuss the effects of ties between people was the German scientist and philosopher Johann Wolfgang von Goethe, where in his classic 1809 novella Elective Affinities speaks of the marriage tie and by analogy shows how strong marriage unions are similar in character to that by which the particles of quicksilver find a unity together though the process of chemical affinity. In 1954, the Russian mathematical psychologist Anatol Rapoport commented on the "well-known fact that the likely contacts of two individuals who are closely acquainted tend to be more overlapping than those of two arbitrarily selected individuals." This arguement became one of the corner stones of the probabilistic approach to network theory. In 1973, stimulate by the work of Rapoport, the American sociologist Mark Granovetter's published The Strength of the Weak Ties, which is recognized as one of the most influential sociology papers ever written.• This picture stuck with him until his graduate school years to inspire his first manuscript on the importance of the weak social ties in human life. He mailed it out in August 1969 to the American Sociological Review. It was rejected, however, because, in the words of two anonymous referees, the manuscript should not be published for "an endless series of reasons that immediately come to mind." In 1972, nevertheless, Granovetter submitted a shortened version to the American Journal of Sociology, and it was finally published in May 1973. According to Current Contents, by 1986, the Weak Ties paper had become a citation classic, being one of the most cited papers in sociology. Tie destinctions Inclusive in the definition of absent ties, according to Granovetter, are those relationships or ties with out substantial significance, such as "nodding" relationships between people living on the same street, or the "tie", for example, to the vendor from whom one customarily buys a morning paper. Moreover, the fact that two people may know each other by name does not necessarily qualify the existence of a weak tie, e.g. if their interaction is negligible the tie may be of the absent variety. The "strength" of an interpersonal tie is a linear combination of the amount of time, the emotional intensity, the intimacy (mutual confiding), and the reciprocal services which characterize each tie. In terms of the possibility of ties carrying more than one stream of information, in 1969 anthropologist Bruce Kapferer, after doing field work in Africa, published his "Norms and the Manipulation of Relationships in a Work Context", in which he postulated the existence of multiplex ties, characterized by multiple contents in a relationship. In telecommunications, a multiplexer is a device that allows a transmission medium to carry a number of separate signals. In social relations, by extrapolation, "multiplexity" is the overlap of roles, exchanges, or affiliations in a social relationship. Research data In Granovetter's original paper, to research the conception of weak ties, he crossed the Charles River to Newton, Massachusetts where he surveyed 282 professional, technical, and managerial workers in total, of which 100 were personally interviewed, in regards to the type of tie between the job changer and the contact person who provided the necessary information. Tie strength was measured in terms of how often they saw the contact person during the period of the job transition, using the following assignment: Of those who found jobs through personal contacts (N=54), 16.7% reported seeing their contact often, 55.6% reported seeing their contact occasionally, and 27.8% rarely. When asked whether a friend had told them about their current job, the most frequent answer was “not a friend, an acquaintance.” The conclusion from this study is that weak ties are an important resource in occupational mobility. When seen from a macro point of view, weak ties play a role in effecting social cohesion. Social networks In social network theory, social relationships are viewed in terms of nodes and ties. Nodes are the individual actors within the networks, and ties are the relationships between the actors. There can be many kinds of ties between the nodes. In its most simple form, a social network is a map of all of the relevant ties between the nodes being studied. Weak tie hypothesis The "weak tie hypothesis" argues, using a combination of probability and mathematics, as originally stated by Anatol Rapoport in 1957, that if A is linked to both B and C, then there is a greater than chance probability that B and C are linked to each other: That is, if we consider any two randomly selected individuals, such as A and B, from the set S = A, B, C, D, E, ..., of all persons with ties to either or both of them, then, for example, if A is strongly tied to both B and C, then according to probability arguments, the B-C tie is always present. The absence of the B-C tie, in this situation, would create, according to Granovetter, what is called the forbidden triad. In other words, the B-C tie, according to this logic, is always present, whether weak or strong, given the other two strong ties. In this direction, the "weak tie hypothesis" postulates that clumps or cliques of social structure will form, being bound predominately by "strong ties", and that "weak ties" will function as the crucial bridge between any two densely knit clumps of close friends. It follows, then, that individuals with few weak ties will be deprived of information from distant parts of the social system and will be confined to the provincial news and views of their close friends. From this basis, other theories can be formulated and tested, e.g. that the diffusion of information, such as rumors, may tend to be dampened by strong ties, and thus flow more easily through weak ties. Positive ties and negative ties Starting in the late 1940s, Anatol Rapoport and others developed a probabilistic approach to the characterization of large social networks in which the nodes are persons and the links are acquaintanceship. During these years, formulas were derived that connected local parameters such as closure of contacts, such as the supposed existence of the B-C tie, to the global network property of connectivity. Moreover, acquaintanceship, in most cases, is a positive tie, but what about negative ties such as animosity among persons? To tackle this problem, graph theory, which is the mathematical study of abstract representations of networks of points and lines, can be extended to include these two types of links and thereby to create models that represent both positive and negative sentiment relations. This effort led to an important and non-obvious Structure Theorem, as developed by Dorwin Cartwright and Frank Harary in 1956, which says that if a network of interrelated positive and negative ties is balanced, e.g. as illustrated by the psychological consistency of "my friend's enemy is my enemy", then it consists of two subnetworks such that each has positive ties among its nodes and negative ties between nodes in distinct subnetworks.Cartwright, Dorwin & Harary, Frank. (1956). "Structural Balance: A Generalization of Heider's Theory." Psychological Review 63:277-293. The imagery here is of a social system that splits into two cliques. There is, however, a special case where one of the two subnetworks may be empty, which might occur in very small networks. In these two developments, we have mathematical models bearing upon the analysis of structure. Other early influential developments in mathematical sociology pertained to process. For instance, in 1952 Herbert Simon produced a mathematical formalization of a published theory of social groups by constructing a model consisting of a deterministic system of differential equations. A formal study of the system led to theorems about the dynamics and the implied equilibrium states of any group. Recent views In the early 1990s, American social economist James Montgomery contributed to economic theories of network structures in labor market. In 1991, Montgomery incorporated network structures in an adverse selection model to analyze the effects of social networks on labor market outcomes. In 1992, Montgomery explored the role of “weak ties”, which he defined as non-frequent and transitory social relations, in labor market. He demonstrates that weak ties are positively related to higher wages and higher aggregate employment rates. See also | ||||||||||
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