Let's say I have a simple graph of undirected, weighted edges. I want to agglomerate nodes one-at-a-time by combining the two nodes which have the highest weighted edge, recalculating remaining edge weights by summing, and iterating. So if the starting graph looks like this:
A and B would be combined, and the weight of the edge from AB-C would be the sum of the original A-C and B-C edges (2+2):
A second iteration would combine AB and C and then we have:
Is there a name for this kind of procedure? I'd like to implement something like this in R. I suspect functions for this already exist somewhere.
Reading about agglomerative hierarchical clustering, K-means, etc., it seems like they're generally performed using dissimilarity measures calculated by comparing vectors of measures associated with the items to be agglomerated, but I don't think that's the same logic for what I have in mind, since I'm using graph data (an adjacency matrix) rather that attribute data. Having trouble finding the right keywords for this. Thank you!