Phylogenetic networks represent the evolutionary process of reticulate organisms by the explicit modeling of gene flow. While most existing network methods are not scalable to tackle big data, we introduce a novel method to reconstruct phylogenetic networks based on algebraic invariants without the heuristic search of network space. Our methodology is available in the Julia package phylo-diamond.jl, and it is at least 10 times faster than the fastest-to-date network methods.