  Networks have in recent years emerged as an invaluable tool for describing
and quantifying complex systems in many branches of science. Recent studies
suggest that networks often exhibit hierarchical organization, where vertices
divide into groups that further subdivide into groups of groups, and so forth
over multiple scales. In many cases these groups are found to correspond to
known functional units, such as ecological niches in food webs, modules in
biochemical networks (protein interaction networks, metabolic networks, or
genetic regulatory networks), or communities in social networks. Here we
present a general technique for inferring hierarchical structure from network
data and demonstrate that the existence of hierarchy can simultaneously explain
and quantitatively reproduce many commonly observed topological properties of
networks, such as right-skewed degree distributions, high clustering
coefficients, and short path lengths. We further show that knowledge of
hierarchical structure can be used to predict missing connections in partially
known networks with high accuracy, and for more general network structures than
competing techniques. Taken together, our results suggest that hierarchy is a
central organizing principle of complex networks, capable of offering insight
into many network phenomena.
