## Mathematical sociology |

**Mathematical sociology** is the area of ^{[1]}

- history
- further developments
- present research
- research programs
- awards in mathematical sociology
- texts and journals
- see also
- references
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Starting in the early 1940s, ^{[2]}^{[3]} and subsequently in the late 1940s, ^{[4]}

Moreover, acquaintanceship is a *positive tie*, but what about *negative ties* such as animosity among persons? To tackle this problem, *balanced* if the product of the signs of all relations in every cycle (links in every graph cycle) is positive. Through formalization by mathematician ^{[5]} 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 is empty, which might occur in very small networks.
In another model, ties have relative strengths. 'Acquaintanceship' can be viewed as a 'weak' tie and 'friendship' is represented as a strong tie. Like its uniform cousin discussed above, there is a concept of closure, called strong triadic closure. A graph satisfies strong triadic closure If A is strongly connected to B, and B is strongly connected to C, then A and C must have a tie (either weak or strong).

n 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 ^{[6]} of

The emergence of mathematical models in the social sciences was part of the zeitgeist in the 1940s and 1950s in which a variety of new interdisciplinary scientific innovations occurred, such as ^{[7]}