  Methods that generate networks sharing a given degree distribution and global
clustering can induce changes in structural properties other than that
controlled for. Diversity in structural properties, in turn, can affect the
outcomes of dynamical processes operating on those networks. Since exhaustive
sampling is not possible, we propose a novel evolutionary framework for mapping
this structural diversity. The three main features of this framework are: (a)
subgraph-based encoding of networks, (b) exact mutations based on solving
systems of Diophantine equations, and (c) heuristic diversity-driven mechanism
to drive resolution changes in the MapElite algorithm. We show that our
framework can elicit networks with diversity in their higher-order structure
and that this diversity affects the behaviour of the complex contagion model.
Through a comparison with state of the art clustered network generation
methods, we demonstrate that our approach can uncover a comparably diverse
range of networks without needing computationally unfeasible mixing times.
Further, we suggest that the subgraph-based encoding provides greater
confidence in the diversity of higher-order network structure for low numbers
of samples and is the basis for explaining our results with complex contagion
model. We believe that this framework could be applied to other complex
landscapes that cannot be practically mapped via exhaustive sampling.

Social and Information Networks;Physics and Society