The book “At the Mercy of the Networks” by Ernesto Estrada offers a unique perspective on how to comprehend complex structures by examining the interconnectedness of their elements. Estrada, a research professor at the Higher Council for Scientific Research (CSIC) at the Institute of Interdisciplinary Physics and Complex Systems, uses mathematical objects such as networks or graphs to simplify relationships between elements through a set of points (vertices) and connections (edges) between them.
In his book, Estrada explores different mathematical models that simulate the formation of social networks and enable a simplified study of real-life network structures. One such model created by mathematicians Paul Erdös and Alfred Rényi begins with a group of individuals who do not know each other, and whether or not a connection is formed between two nodes is determined by a random value compared to a threshold value.
To determine if the simulation results resemble real-world social networks, one can analyze key characteristics such as network density, connectivity, and the average length of pathways between elements. These properties shed light on how information flows within the network. Many real-world social networks display characteristics such as high connectivity and low density, allowing information to be transmitted across vast networks efficiently.
However, measuring the distance of the shortest paths between elements can illustrate