We are developing a sequencing-based microscopy technique, in which spatial molecular positions are determined not with optics, but by reconstructing networks of DNA barcodes. The interactive panel here is an example of a simulated, spatially informative network. If you zoom in to the cloud of nodes and edges, we can see that edges are drawn between spatially neighboring nodes. This means that edges are correlated with spatial proximity. In this case, the relationship is very strong, but even when this correlation is weaker, it is possible to use this to our advantage to infer spatial information from network structure.
Understanding what makes a network spatially informative
A network is simply a set of objects that are connected, and in its simplest form, is just a list of those connections. An example of this might be big list of regional transit connections in Europe, e.g. Stockholm to Copenhagen or Paris to Lyon. A network is "spatial" if those connections are related to the distance between objects. So a list of regional transit connections in fact gives us information about where, in space, the cities are located relative to one another. By optimizing for satisfaction of constraints, i.e. maximizing the closeness of connected nodes, we can recover that spatial information and generate an approximation - have a look at the interactive plot here. -> We can see a few things - first of all the global positions have not be preserved. However try reflecting and rotate this image, and you should be able to arrive at a more familiar map of Europe. Considering that no information about coordinates was passed through to this reconstruction, we should be impressed!