The network approach to nature

Networks are all around us, and we are ourselves, as individuals, the units of a network of social relationships of different kinds and, as biological systems, the delicate result of a network of biochemical reactions. Networks can be tangible objects in the Euclidean space, such as electric power grids, the Internet, highways or subway systems, and neural networks . Or they can be entities defined in an abstract space,such as network so between individuals.

Since its birth in 1736,
when the Swiss mathematician Leonhard Euler published the solution to the Königsberg bridge problem (consisting in finding a round trip that traversed each of the bridges of the prussian city of Königsberg exactlyonce),graph theory has witnessed many exciting developments and has provided answers to a series of practical questions such as: what is the maximum flow per unit time from source to sink in a network of pipes, how to color the regions of a map using the minimum number of colors so that neighboring regions receive different colors, or how to fill n jobs by n people with maximum total utility. In addition to the developments in mathematical graph theory, the study of network has seen important achievements in some specialized contexts,as for instance in the social sciences. Social networks analysis started to develop in the early 1920s and focuses on relationships among social entities, as communication between members of a group, trades among nations, or economic transactions between corporations.

These include transportation networks, phone call networks, the Internet and the World Wide Web, the actors’ collaboration network in movie databases, scientific coauthorship and citation networks from the Science Citation Index, but also systems of interest in biology and medicine, as neural networks or genetic, metabolic and protein networks. The massive and comparative analysis of networks from different fields has produced a series of unexpected and dramatic results. The first issue that has been faced is certainly structural. The research on complex networks begun with the effort of defining new concepts and measure to characterize the topology of real networks.