Historically, the success of science has depended on the idea of dividing systems into their basic units. However, to understand complex structures, it is necessary to adapt another perspective, allowing us to understand the interconnections between the elements that compose them.
Ernesto Estrada, Research Professor at the Superior Council for Scientific Research (CSIC) of the Institute of Interdisciplinary Physics and Complex Systems, in Spain, in his work At the Mercy of Networks, described social networks in a mathematical way, through a set of points – called vertices – and unions – called edges. . This model allows you to capture important information from a myriad of real-world situations: social relationships, epidemics, anatomical structures, genetic, metabolic or neural networks, social conflicts or transport networks.
However, the network that offers the greatest mathematical analysis is the first social networks. In this case, the points are people and the vertices can be mutual knowledge, friendship or cooperation.
Estrada mentioned several mathematical models that simulate the formation of social networks and that allow us to study real network structures in a simplified way. The first, developed by mathematicians Paul Erdös and Alfred Rennie, starts from n of previously unknown individuals – so, initially it has n vertices and no edges – and a number k that indicates how conducive the environment is to establishing relationships. In each simulation, each pair of ‘n’ is assigned a random value; If it is greater than ‘k’, a vertex is created between these two vertices; If it’s smaller, no.
To evaluate whether the result obtained is similar to that observed in real-world social networks, it can be checked whether the main characteristics of real-world networks have been preserved. These properties allow us to understand the dynamics of a network, that is, how information is transferred within it. One of them is network density, which corresponds to the number of connections between elements. It is the percentage of the number of connections there are, compared to all the connections that could be on the network. If all elements are connected to the rest, the network is complete.
According to Estrada, almost all social networks in the world are practically connected. For example, 92.2% of authors in the biomedical sciences are related – in this case, meaning they have a shared publication in the Medline Articles database – with each other, while in mathematics 82% (using the Mathematical Reviews Database). This means that information can be transferred between almost all members of the network.
Moreover, they are very sparse: the density of none of the previous networks exceeds 0.02%; In other words, everyone doesn’t have to be in touch with everyone.
In a connected network, we can calculate the distance of the shortest path connecting each pair of elements: for example, if Ana and Carlos do not cooperate, but Ana cooperates with Beatriz, who does with Carlos, then the distance between Ana and Carlos is 2. The average of these The values - called the average single path length, ‘L’ – are the number of steps you generally have to take to get from one point in the network to another.
In the vast majority of real-world social networks, this number is surprisingly small – for example, 4.6 in the Biomedical Sciences Collaboration Network. This is known as the small-world effect or the six-degree theory of separation.
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