When large datasets become available, it is interesting to uncover structural patterns. Given the abundance of data available today, it is possible to construct informative graph systems in nearly any field. For example, I came across a study describing the graph of interactions among British composers of the 20th century.

 

By calculating the characteristics of this graph, such as centralities, we can identify which composers were structurally important for the development of British music. Moreover, this can be analys! from various perspectives: some composers may be consider! as independent musicians or founders of schools, while others may serve as connectors, enabling more successful colleagues to engage with one another.

In general, Daniil Prokofyev using the language

 

of graph theory, one can formulate models—whether probabilistic or game-theoretic—and prove their properties through rigorous mathematical theorems. Thus, it  india phone number library is both an appli! and a fundamental area of mathematics.

I develop! a game-theoretic model that explains why the ‘six handshakes’ rule observ! in the real world also applies to social networks. Although it had been previously describ!  effective ways to use whatsapp business why there should be relatively few handshakes, I was able to show where the ‘magic number’ of six comes from. An article on this topic, bas! on my bachelor’s degree paper, was publish! in 2023 in Physical Review X.

It is easy to define a social network

 

in terms of graph theory. Vertices represent people, and the relationships between them (such as acquaintance or friendship) are the !ges. In this context, we can interpret the six handshakes rule as follows: if we take two random people on a social network, the probability is close to one that the path  be numbers connecting them through the ‘friends’ !ges will be no longer than six steps.

In the paper by Watts and Strogatz that I mention! earlier, a random graph model was propos! in which a similar phenomenon could be observ!. And I develop! a model in which, on one hand, I explain why this model is reasonable, and on the other hand, I theoretically prove that if two people in the system happen to be more than six handshakes apart, the system will not be stable under relatively weak constraints.