Interpersonal ties

One of the earliest writers to describe the nature of the ties between people was German scientist and philosopher, Johann Wolfgang von Goethe. In his classic 1809 novella, Elective Affinities, Goethe discussed the "marriage tie". The analogy shows how strong marriage unions are similar in character to particles of quicksilver, which find unity through 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 argument became one of the cornerstones of social network theory. In 1973, stimulated by the work of Rapoport and Harvard theorist Harrison White, Mark Granovetter published The Strength of Weak Ties. To obtain data for his doctoral thesis, Granovetter interviewed dozens of people to find out how social networks are used to land new jobs. Granovetter found that most jobs were found through "weak" acquaintances. This pattern reminded Granovetter of his freshman chemistry lesson that demonstrated how "weak" hydrogen bonds hold together many water molecules, which are themselves composed of atoms held together by "strong" covalent bonds. In Granovetter's view, a similar combination of strong and weak bonds holds the members of society together. 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 1970, Granovetter submitted his doctoral dissertation to Harvard University, entitled "Changing Jobs: Channels of Mobility Information in a Suburban Community". 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 affecting 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 simplest 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 may follow that individuals with few bridging 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. However, having a large number of weak ties can mean that novel information is effectively "swamped" among a high volume of information, even crowding out strong ties. The arrangement of links in a network may matter as well as the number of links. Further research is needed to examine the ways in which types of information, numbers of ties, quality of ties, and trust levels interact to affect the spreading of information. there are some problems in the Granovetter definition. The first one refers to the fact that the Granovetter definition of the strength of a tie is a curvilinear prediction and his question is "how do we know where we are on this theoretical curve?". The second one refers to the effective character of strong ties. Krackhardt says that there are subjective criteria in the definition of the strength of a tie such as emotional intensity and the intimacy. He thought that strong ties are very important in severe changes and uncertainty: He called this particular type of strong tie philo and define philos relationship as one that meets the following three necessary and sufficient conditions: • Interaction: For A and B to be philos, A and B must interact with each other. • Affection: For A and B to be philos, A must feel affection for B. • Time: A and B, to be philos, must have a history of interactions with each other that have lasted over an extended period of time. The combination of these qualities predicts trust and predicts that strong ties will be the critical ones in generating trust and discouraging malfeasance. When it comes to major change, change that may threaten the status quo in terms of power and the standard routines of how decisions are made, then trust is required. Thus, change is the product of philos. 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, and the supposed existence of the B–C tie to the global network property of connectivity. which was published by Frank Harary in 1953. A signed graph is called balanced if the product of the signs of all relations in every cycle is positive. A signed graph is unbalanced if the product is ever negative. The theorem says that if a network of interrelated positive and negative ties is balanced, then it consists of two subnetworks such that each has positive ties among its nodes and negative ties between nodes in distinct subnetworks. In other words, "my friend's enemy is my enemy". 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 the structure. Other early influential developments in mathematical sociology pertained to process. For instance, in 1952 Herbert A. 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. Absent or invisible ties In a footnote, Mark Granovetter defines what he considers as absent ties: The concept of invisible tie was proposed to overcome the contradiction between the adjective "absent" and this definition, which suggests that such ties exist and might "usefully be distinguished" from the absence of ties. ==The individualistic perspective==

Granovetter's 1973 work proved to be crucial in the individualistic approach of the social network theory as seen by the number of references in other papers. His argument asserts that weak ties or "acquaintances", ==Labour market==

In the early 1990s, US social economist James D. Montgomery contributed to economic theories of network structures in the labour market. In 1991, Montgomery incorporated network structures in an adverse selection model to analyze the effects of social networks on labour market outcomes. In 1992, Montgomery explored the role of "weak ties", which he defined as non-frequent and transitory social relations in the labour market. He demonstrated that weak ties are positively correlated with higher wages and higher aggregate employment rates. ==See also==