We are currently working at the intersection of metaheuristics and machine learning.
As part of the scheduling problem that we are trying to solve, we have a project network (directed acylic graph) that captures the precedence relations between different activities that are to be scheduled.
Now we want to use this project network as a feature for a machine learning approach. One idea that came to mind is to use the adjacency matrix or reachability matrix as feature vectors for the machine learning model. Our intention is to capture the complete network structure as a feature and not just some "aggregating" measures such as density of transitive closure or ratio of nodes to arcs, etc.
The problem that we encounter is that depending on the labeling of the nodes, two identical project networks may have adjacency matrices that look very different. Ideally however, if the project networks are identical, the adjacency matrices should also be identical, independent of the labeling of the nodes.
We therefore propose to re-name the nodes according to some predefined logic. One could, for example, take into consideration the number of immediate or transitive successors.
Is anyone familiar with an approach like that or could guide us into the right direction with e.g. search terms to search for? The goal is to have a representation of the network that is invariant of the node labels.
Maybe research in the area of image processing would have to be something to look at? This may sound very "layman" but in the end it seems similar to the problem of having a single object but images of different perspectives. However, now we have the chance to "orient" the object in a predefined way (in this case by relabeling the nodes). Please excuse the clunky explanation.
For a visual help, I have drawn a quick sketch that illustrates the problem: Even though the networks are identical, the adjacency matrices are quite different: