Imaging-by-sequencing methods are an emerging alternative to conventional optical micro- or nanoscale imaging. In these methods, molecular networks form through proximity-dependent association between DNA molecules carrying random sequence identifiers. DNA strands record pairwise associations such that network structure may be recovered by sequencing which, in turn, reveals the underlying spatial relationships between molecules comprising the network. Determining the computational reconstruction strategy that makes the best use of the information (in terms of spatial localization accuracy, robustness to noise, and scalability) in these networks is an open problem. We present a graph-based technique for reconstructing a diversity of molecular network classes in 2 and 3 dimensions without prior knowledge of their fundamental generation mechanisms. The model achieves robustness by obtaining an unsupervised sampling of local and global network structure using random walks, making use of minimal prior assumptions. Images are recovered from networks in two stages of dimensionality reduction first with a structural discovery step followed by a manifold learning step. By breaking the process into stages, computational complexity could be reduced leading to fast and accurate performance. Our method represents a means by which diverse molecular network generation scenarios can be unified with a common reconstruction framework.