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http://www.learner.org/courses/mathilluminated/units/2/textbook/06.php

Combinatorics, the mathematics of organization, shows very similar reasoning methods with the networks theory studied in class. Combinatorics is the branch of mathematics that is central to basic problems inherent in our data-rich age; it is the quest to uncover relational meaning among the members of those sets.

More specifically, the Ramsey theory shows mathematically that structure must exist in randomness. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures. Just as Mark Granovetter developed the theory of the strong triadic closure to explain the job search through acquaintances, Ramsey observed in the ‘Party Problem’, that in any group of six people, it is mathematically guaranteed to find either three mutual friends or three mutual strangers.

In the party problem, Ramsey uses a complete graph where all nodes are linked by an edge. The links are positive or negative (blue or Red in the online article). They do not denote friendship and antagonism but simply mutual friends and mutual strangers.

In the complete graph of six nodes, each vertex has five connections. To attempt to disprove the theory, the article focuses on the triangles formed among the connections of each vertex. However, when observing all the possible triangle combination, it is observed that at least one of the triangles has to have all edges of the same sign, proving that among the six party goers there will be at least a group of three friends or a group of three strangers.

 

Jean-Herve

 

 

 

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