Complex Networks for a Complex Century

The ultra-fast progress in science and technology in the 21st century has revealed a variety of complexities pertain to both understanding the systems’ behaviors (current states) as well as their predictions (future states). In fact, Stephen Hawking, stated: “I think the next century will be the century of complexity.” In general, complex systems are composed of highly interconnected entities that follow simple rules of operation by which the system shows complex collective behaviors, such as self-organization with no leader. For example, many ants together can build structures like bridges and organize their colonies without a leader ant. Another example is our ability to transfer complicated information by combining the words of a language.

The common traits of complex systems are interconnectivity, self-adaptation, self-organization, hard-to-predict, non-linearity, and being consist of many heterogeneous entities. The central question of the science of complex systems is how emergent characteristics such as self-organization occur in these systems? One of the keys to finding an answer to this question is the science of networks.

A network has a simple structure: nodes representing the entities of a system and links that capture the connections between these entities. Examples of networks abound in natural and man-made complex systems, including the veins of a leaf (Fig. 1), brain’s neural connections, the World Wide Web, and airline networks. In fact, living systems are commonly described as information processing networks. Perhaps one of the most famous examples of networks is the six degrees of separation, a theory that any two persons in the world are reachable by a chain of “a friend of friend” with just six steps, representing the small-world phenomenon observed in human society. The importance of networks arises from the way of thinking behind it that is focusing on the relationships between the entities rather than the entities themselves. For instance, consider the fact that humans and some plants have about 25,000 genes. Having around the same number of genes does not reflect the biological complexity of humans compared to the plants. Many biologists believe the complexity of an organism arises from the complexity in the interactions between its genes. The great genome project provided us with the book of life containing the list of all genes, and networks are providing the map of life that describes the dynamics in which genes interact with each other.

Fig 1. Biological and man-made networks

Large complex systems behave in ways that reflect their structure. With the exponential growth of computational power within past decades, for the first time in human history, we can capture the complex networks behind the structure and dynamics of complex systems. Soon scientists realized that networks with their real-world relevance, complex dynamics, and rigorous mathematical characteristics are the perfect vehicle to model complex systems. The new science of networks emerged as a highly interdisciplinary field connecting many disciplines that were thought to be independent of each other. By applying network thinking, scientists could tackle challenging problems such as understanding the role of scale, diversity, failure, and innovation in the formation, sustainability, and growth of complex systems. In biology, scientists have recently developed a theorem to explain the well-known relationship between body mass and metabolic-rate. The amount of heat produced by an organism can be predicted solely by its body mass (kg). The name of this is called metabolic scaling theory that arose from viewing the blood circulatory system of organisms as a network and analyzing the structure of such a network. Another recent work in the science of success discovered universal laws of success from analyzing very large networks of scientific collaborations, art exhibitions, athletic competitions, etc. This analysis resulted in a model that predicts the Nobel prize winners with high accuracy from scientific collaboration networks. From studying the dynamics of networks, we can predict whether a disease can turn into an epidemic, how a few malfunctions can cause a cascading power failure, and understand the outbreak of revolutions. Moreover, social scientists employed network thinking to explore the role of diversity and network ties on the emergence of collaboration and innovation over time.

Many more magnificent works highlight networks' role in explaining and discovering the extraordinary commonalities behind complex systems, such as the mentioned scaling relationship between the body mass and metabolic rate. This blog is a contemplation on the role of network thinking in our journey toward solving the challenging problems of the 21st century. Adopting network thinking provides a new perspective to look at complex systems. When Einstein was asked what was most helpful to him in developing the theory of relativity, he replied: “Figuring out how to think about the problem.