Formation of network modules by dual phase evolution

Modular structure is the most common way of managing complexity in large systems, but how modules emerge in self-organizing systems is poorly understood. Here we show that in complex networks, modules can form spontaneously under dual phase evolution (DPE), a process in which a system repeatedly flips between a weakly connected ldquobalancerdquo phase and a richly connected ldquovariationrdquo phase. By creating and preserving stable components but still permitting variation, DPE makes it possible to direct self-organization into creating a wide variety of different forms.