Science has long relied on the concept of breaking down systems into their fundamental components to understand complex structures. However, a new approach is needed to comprehend the interconnectedness of elements within these structures. This is the focus of a book by Ernesto Estrada, a research professor at the Higher Council for Scientific Research (CSIC) at the Institute of Interdisciplinary Physics and Complex Systems.
In his book, Estrada explores the mathematical object known as networks or graphs, which simplify relationships between elements by using a set of points (vertices) and connections (edges) between them. These networks can capture essential information from various real-life scenarios such as social relations, epidemics, anatomical structures, gene metabolic or neuronal networks, social conflicts, and transportation networks.
Estrada discusses different mathematical models that simulate network formation and allow researchers to study real-life network structures in a simplified manner. One such model created by mathematicians Paul Erdös and Alfred Rényi begins with individuals who do not know each other and determines whether or not a connection is formed based on 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 average pathway length between elements. These properties shed light on how information flows within the network. Many real-world social networks exhibit characteristics such as high connectivity and low density, allowing information to be transmitted efficiently across vast networks.
Another model proposed by scientists like Steven Strogatz better captures certain real-world social network characteristics such as transitivity. The study of these models offers valuable insights into the complexity of social phenomena that would be challenging to obtain through other means.
Overall, graph theory provides researchers with a unique perspective on how elements interact and influence each other within complex systems. It also highlights the importance of understanding interconnectedness in comprehending how information flows within these systems.
In conclusion, science’s success has been rooted in breaking down complex systems into their fundamental units. However, adopting a perspective that allows us to grasp interconnectedness is crucial for understanding how these systems function fully.
As research professor at CSIC’s Institute of Interdisciplinary Physics and Complex Systems Ernesto Estrada demonstrates this through his book “At the Mercy of Networks.” In it he explores mathematical objects known as networks or graphs that simplify relationships between elements through sets of points (vertices) and connections (edges) between them.
Estrada discusses different mathematical models that simulate network formation and allow researchers to study real-life network structures in simplified ways. For instance, he highlights Paul Erdös and Alfred Rényi’s model that begins with individuals who do not know each other determined whether or not a connection is formed based on random values compared to threshold values.