Summary: Is there a way to "identify" nodes between graphs (not on the same graph) from a set of graphs, not knowing the identity of any at first, using edges weights and node features?
I'm new to graph theory and facing a problem that might already have a solution, but I didn't find one on the net yet:
- I have a set a fully connected undirected graphs
- Edges are weighted and nodes have features
- The graphs have roughly the same number of nodes, but not exactly
- The graphs should be mostly equivalent (most of the time, it is possible to find equivalent nodes in the other graphs for a given node in one graph)
- BUT, for each graph, the "identity" of the nodes is unknown.
The problem is then to find the identity of the nodes (or lack thereof for nodes with no equivalent in other graphs), using the information on the edges and the nodes.
But since the identity of each node is unknown, I find it hard to use the information in edges weight. For now, the only only possible solution I see is to use the nodes features to first estimate a probable identity, then confirm it or disprove it using the edges weight patterns that arise from such putative identity. And repeat the process until I find a satisfying solution.
I find this quite inelegant (and time consuming), so if you know any other way, it would be great!
Thanks in advance!
PS: For those interested, this problem arises from brain functional connectivity. I have a set of subjects with estimated brain areas (nodes) and their functional relationships (edges). I have the localization of each area (node features), but it varies quite a bit between subject and is far from perfect when it come to identifying equivalent areas in different brains. This is why I want to use the edges value to get a better estimation of equivalent areas between subjects.