Multiscale network generation

Relationships between entities in complex systems could be represented using the paradigm of networks. The network representation can then reveal the evolution, structure and dynamics of those systems. Frequently, obtaining the required scientific data about the networks is expensive or infeasible. In other words, the amount of available empirical data is insufficient for simulation, validation, verification, and other scientific tasks. In these situations, empirical data should be augmented by synthetic data generated from models in such a way that properties of the system are preserved in the synthetic data, even when those properties are unique to the system or not fully known, but existing methods only reproduce a limited set of specified network properties. Here we introduce a novel strategy for synthesizing artificial networks that can realistically model a variety of network properties and that is termed multiscale network generation, or as a specific algorithm, MUSKETEER. This strategy first creates a hierarchy of aggregated representations of the original network, and then reformulates the network generation problem at all levels of this hierarchy in order to take into account properties at multiple scales of the system. The network is then edited at any or all scales, depending on the desired variability in the ensemble of synthetic networks. We find that for many complex networks taken from real-world systems, the strategy is able to preserve important properties with little statistical bias while achieving high degree of variability and arbitrary difference from the original.