In the context of
network theory, a
complex network is a
network (
graph) with non-trivial
topological features—features that do not occur in simple networks such as
lattices or
random graphs. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks such as
computer networks and
social networks.
Most social, biological, and technological networks display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity among vertices, community structure, and hierarchical structure. In the case of directed networks these features also include reciprocity, triad significance profile and other features. In contrast, many of the mathematical models of networks that have been studied in the past, such as lattices and random graphs, do not show these features.
Two well-known and much studied classes of complex networks are scale-free networks and small-world networks, whose discovery and definition are canonical case-studies in the field. Both are characterized by specific structural features—power-law degree distributions for the former and short path lengths and high clustering for the latter. However, as the study of complex networks has continued to grow in importance and popularity, many other aspects of network structure have attracted attention as well.
The field continues to develop at a brisk pace, and has brought together researchers from many areas including mathematics, physics, biology, computer science, sociology, epidemiology, and others. Ideas from network science have been applied to the analysis of metabolic and genetic regulatory networks, the design of robust and scalable communication networks both wired and wireless, the development of vaccination strategies for the control of disease, and a broad range of other practical issues. Research on networks has seen regular publication in some of the most visible scientific journals and vigorous funding in many countries, has been the topic of conferences in a variety of different fields, and has been the subject of numerous books both for the lay person and for the expert.
