Functional complexity index for metabolic and genetic networks

We propose a functional complexity index as a quantitative measure for the inequivalent functions a network can perform. It is sensitive to the information on regulatory rules which may be stored in the network topology and to the dynamical constraints of the network. The topological diversity is formulated by means of “resolutions” of vertices and an induced rewiring of the edges of the corresponding graph. The index allows for the identification of functional hierarchies. It is supposed to be particularly useful for metabolic and genetic networks and allows for a classification of networks in artificial or biological systems, where functionality plays an important role.