Our lives cannot be imagined without polymer networks, which range widely, from synthetic rubber to biological tissues. Their properties—elasticity, strain-stiffening and stretchability—are controlled by a convolution of chemical composition, strand conformation and network topology. Yet, since the discovery of rubber vulcanization by Charles Goodyear in 1839, the internal organization of networks has remained a sealed ‘black box’. While many studies show how network properties respond to topology variation, no method currently exists that would allow the decoding of the network structure from its properties. We address this problem by analysing networks’ nonlinear responses to deformation to quantify their crosslink density, strand flexibility and fraction of stress-supporting strands. The decoded structural information enables the quality control of network synthesis, comparison of targeted to actual architecture and network classification according to the effectiveness of stress distribution. The developed forensic approach is a vital step in future implementation of artificial intelligence principles for soft matter design.