Load-path-based topology optimization is used to synthesize a compliant adaptive aircraft wing leading edge, which deforms in a prescribed way when subject to a single point internal actuation. The load-path-based optimization method requires the specification of a parent lattice. Increasing the complexity of this lattice means the number of parameters required for a complete representation of the structure in the topology optimization becomes prohibitive, although it is desirable to enable a full exploration of the design space. A new method based on graph theory and network analysis is proposed, which enables a substantial reduction in the required number of parameters to represent the parent lattice. The results from this load-path-based approach are compared with those obtained from the better-known density-based topology optimization method.