Modern experiments in many disciplines generate large quantities of network (graph) data. Researchers require aesthetic layouts of these networks that clearly convey the domain knowledge and meaning. However, the problem remains challenging due to multiple conflicting aesthetic criteria and complex domain-specific constraints. In this article, we present a strategy for generating visualizations that can help network biologists understand the protein interactions that underlie processes that take place in the cell. Specifically, we have developed Flud, a crowd-powered system that allows humans with no expertise to design biologically meaningful graph layouts with the help of algorithmically generated suggestions. Furthermore, we propose a novel hybrid approach for graph layout wherein crowd workers and a simulated annealing algorithm build on each other’s progress. A study of about 2,000 crowd workers on Amazon Mechanical Turk showed that the hybrid crowd–algorithm approach outperforms the crowd-only approach and state-of-the-art techniques when workers were asked to lay out complex networks that represent signaling pathways. Another study of seven participants with biological training showed that Flud layouts are more effective compared to those created by state-of-the-art techniques. We also found that the algorithmically generated suggestions guided the workers when they are stuck and helped them improve their score. Finally, we discuss broader implications for mixed-initiative interactions in layout design tasks beyond biology.