<P> Systems exhibit complexity when difficulties with modeling them are endemic . This means their behaviors cannot be understood apart from the very properties that make them difficult to model, and they are governed entirely, or almost entirely, by the behaviors those properties produce . Any modeling approach that ignores such difficulties or characterizes them as noise, then, will necessarily produce models that are neither accurate nor useful . As yet no fully general theory of complex systems has emerged for addressing these problems, so researchers must solve them in domain - specific contexts . Researchers in complex systems address these problems by viewing the chief task of modeling to be capturing, rather than reducing, the complexity of their respective systems of interest . </P> <P> While no generally accepted exact definition of complexity exists yet, there are many archetypal examples of complexity . Systems can be complex if, for instance, they have chaotic behavior (behavior that exhibits extreme sensitivity to initial conditions), or if they have emergent properties (properties that are not apparent from their components in isolation but which result from the relationships and dependencies they form when placed together in a system), or if they are computationally intractable to model (if they depend on a number of parameters that grows too rapidly with respect to the size of the system). </P> <P> The interacting components of a complex system form a network, which is a collection of discrete objects and relationships between them, usually depicted as a graph of vertices connected by edges . Networks can describe the relationships between individuals within an organization, between logic gates in a circuit, between genes in gene regulatory networks, or between any other set of related entities . </P> <P> Networks often describe the sources of complexity in complex systems . Studying complex systems as networks therefore enables many useful applications of graph theory and network science . Some complex systems, for example, are also complex networks, which have properties such as power - law degree distributions that readily lend themselves to emergent or chaotic behavior . The fact that the number of edges in a complete graph grows quadratically in the number of vertices sheds additional light on the source of complexity in large networks: as a network grows, the number of relationships between entities quickly dwarfs the number of entities in the network . </P>

What do you mean by hierarchy of complex systems