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.