Network science is in great need of algorithms that can analyze increasingly larger networks fast. However, this ambition is undermined by the recent theory of fine-grained complexity. It predicts tight (conditional) lower bounds on the complexity of graph distance, counting, and enumeration problems that underlie network science. These lower bounds, while polynomial, are too high for the staggering size of modern data sets. Fortunately, the lower bounds may be circumvented by parameterized algorithms. Still, we lack systematic studies into the effectiveness of this approach. In particular, commonly studied parameters are linear in the input size for standard models of networks. Hence, current parameterized algorithms might not yield the urgently needed improvements to analyze current and future real-world networks. The proposal aims to design new parameterized algorithms to enable the analysis of huge networks. The proposal will initiate a design cycle to discover, analyze, exploit, and validate new parameters geared towards the graphs and problems commonly encountered in network science. This will be achieved through interaction with domain experts, the analysis of data and mathematical models, and building the required algorithmic knowledge of parameterized computation within P. The project will yield a parameter ecology for polynomial-time problems and implementations of the discovered algorithms. In doing so, the proposal seamlessly integrates fundamental research and practical considerations, and may impact the many application areas of network science.