I am looking for some help regarding network theory. Maybe there are just some buzzwords / keywords I don't know and I hope you can help me to find the correct term for my future research.
So, I am looking for a metric to find equal distributed nodes inside a graph. To be more precise, I want to find central/well connected nodes that are equalyl distributed. I know different centrality measures, but theses measures aim for centrality, hence they will be over represented in the center of a graph.
My idea was to first use natural cuts or something similar to split a graph into smaller subgraphs/communities/cuts and then make use of any centrality measures.
Is there a more elegant solution?
For a better understanding: Given is a multidigraph, representing a road network (fixed nodes). The task is to find 'central'/ well connected nodes like transportation hubs, with the condition, that they cover every region of the graph equally. With equal distributed I mean the distance on the graph (edgeweight).
I don't have any starting node. I don't know if it's feasible to calculate reachability or something similiar for every node in the graph.
Update: To make it more clear I try to use an example. Given is a road network of a city. The city has different districts. I try to find the most central nodes for each district. You can exchange the word 'district' with 'region','natural cut' or 'subgraph'. In the end I need a subset of nodes, that represents the differents districts equally (one central node for each district).
Thanks alot in advance for help/feedback!
Some formal buzzwords are "facility location" and even more specifically "metric k-center/vertex k-center", where you minimize the maximum distance/sum of distances to selected hubs. But I suppose you'll find more practical stuff starting from cluster analysis, specifically k-means clustering and variants, or community detection.