Networks

The mathematical characteristics of networks, such as the degree of clustering or the amount of nodes with a certain number links, can indeed tell you how it the network was grown. 

An example of this are the so-called "scale-free" networks, that have a few well connected hubs and a large amount of nodes with few links. They typically grow by attaching a new node preferentially to nodes that already have many links. Our jump gate network has some of these properties, but cannot be really classified as a scale-free network. It also has characteristics of a "dendritic" network, where new links are cast out to explore a vaster amount of space. But again, it is not purely of this form. My mathematician friend confirms that the most likely way that the stargate network formed is by exploration that occasionally stumbled on highly connected remnants of pre-existing links. 

So, highly connected clusters far away from the Empire's home worlds, and far away from economic hubs, should be a good indication of homeworlds for ancient cultures.

I was also told that there are many different measures by which to judge the strategic importance of a node (or a system in our case). It's not always the node with the most links that is the more imporant. Other so-called "measures of node centrality" may apply such as how often a certain node lies on the shortest route between any two other random nodes. It would be interesting to find out which of the many measures of centrality would explain why Jita and Dodoxie grew to some importance in trading. 

Of course, why Amarr is important and always will be requires no explanation.