Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms, is robust and uses a linear number of links. Rather than providing a concrete network model, we take an axiom-based design approach. We provide three intuitive and independent algorithmic axioms and prove that any network that satisfies all axioms enjoys an efficient algorithm for a range of tasks (such as MST, sparse matrix multiplication, and more). We also show the necessity of our axiom set: for networks that satisfy any subset of the axioms, the same efficiency cannot be guaranteed for any deterministic algorithm. (C) 2016 Elsevier Inc. All rights reserved.