We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures providing additional information, while the composite centrality measure tends to the standard normal distribution. This offers a unified scale to measure node and edge centralities for complex evolving networks under a uniform framework. Considering two real-world cases of the world trade web and the world migration web, both during a time span of 40 years, we propose a standard set-up to demonstrate its remarkable normative power and accuracy. We illustrate the applicability of the proposed framework for large and arbitrary complex systems, as well as its limitations, through extensive numerical simulations.