EDIT: After some more tests, I now realise that this is not really as great a vertex label/descriptor as I thought it was. For example, see these four graphs on 7 vertices that fail to distinguish vertices properly:

The first one should have a central vertex in a different class than the other blue vertices. The green class in the second graph should be split, and same for the third graph. And so on.

So, in the last post I talked about the ideas of RandiÄ‡ et al for calculating the 'centrality' of vertices in a graph. Interestingly, the numbers calculated for each vertex act as a kind of equivalence class label or vertex invariant. This is similar in many ways to Morgan numbers (sorry, Egon's post doesn't actually explain them, but they are the sum of degrees across extended neighbourhoods).

For example, here is one of the examples from the previous post:

With the centrality matrix in the middle, and the 'label' made by sorting the row elements in descending ord…

The first one should have a central vertex in a different class than the other blue vertices. The green class in the second graph should be split, and same for the third graph. And so on.

So, in the last post I talked about the ideas of RandiÄ‡ et al for calculating the 'centrality' of vertices in a graph. Interestingly, the numbers calculated for each vertex act as a kind of equivalence class label or vertex invariant. This is similar in many ways to Morgan numbers (sorry, Egon's post doesn't actually explain them, but they are the sum of degrees across extended neighbourhoods).

For example, here is one of the examples from the previous post:

With the centrality matrix in the middle, and the 'label' made by sorting the row elements in descending ord…