  The structure of the network underlying many complex systems, whether
artificial or natural, plays a significant role in how these systems operate.
As a result, much emphasis has been placed on accurately describing networks
using network theoretic metrics. When it comes to generating networks with
similar properties, however, the set of available techniques and properties
that can be controlled for remains limited. Further, whilst it is becoming
clear that some of the metrics currently used to control the generation of such
networks are not very prescriptive so that networks could potentially exhibit
very different higher-order structure within those constraints, network
generating algorithms typically produce fairly contrived networks and lack
mechanisms by which to systematically explore the space of network solutions.
In this paper, we explore the potential of a multi-objective novelty-biased GA
to provide a viable alternative to these algorithms. We believe our results
provide the first proof of principle that (i) it is possible to use GAs to
generate graphs satisfying set levels of key classical graph theoretic
properties and (ii) it is possible to generate diverse solutions within these
constraints. The paper is only a preliminary step, however, and we identify key
avenues for further development.
