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Methods that generate networks sharing a given degree distribution and globalclustering can induce changes in structural properties other than thatcontrolled for. Diversity in structural properties, in turn, can affect theoutcomes of dynamical processes operating on those networks. Since exhaustivesampling is not possible, we propose a novel evolutionary framework for mappingthis structural diversity. The three main features of this framework are: (a)subgraph-based encoding of networks, (b) exact mutations based on solvingsystems of Diophantine equations, and (c) heuristic diversity-driven mechanismto drive resolution changes in the MapElite algorithm. We show that ourframework can elicit networks with diversity in their higher-order structureand that this diversity affects the behaviour of the complex contagion model.Through a comparison with state of the art clustered network generationmethods, we demonstrate that our approach can uncover a comparably diverserange of networks without needing computationally unfeasible mixing times.Further, we suggest that the subgraph-based encoding provides greaterconfidence in the diversity of higher-order network structure for low numbersof samples and is the basis for explaining our results with complex contagionmodel. We believe that this framework could be applied to other complexlandscapes that cannot be practically mapped via exhaustive sampling.

Mapping structural diversity in networks sharing a given degree  distribution and global clustering: Adaptive resolution grid search evolution  with Diophantine equation-based mutations