Measuring Importance in Movement

One way to measure the importance of a node in a network/system is “betweenness centrality”.

Betweenness determines importance based on how well a particular "node" serves as a bridge between other nodes - that is, which node provides the shortest path possible between all nodes, with the fewest steps possible.

The node with most “betweenness” provides the FEWEST steps possible, between ALL the nodes.

In the attached graph, it is the BLUE nodes that are the most central, because on average, these nodes represent bridges along the shortest paths for ALL elements, on average. The red nodes represent the opposite.

As an analogy, imagine a city street. It has betweenness if it's most accessible from all other city streets. If a city street is easy to get to from only one place, then it's low in this betweenness centrality (and red, on our graph, and hence pushed towards the periphery). If you count the number of "edges" (connections) from the nodes with various colors, you can see that color generally corresponds with number of connections (but not in a 1:1 fashion).

So take at a one arm handstand: so much time invested, and yet… how many connections does it serve, in the big picture? At best, it yields low to moderate in “betweenness centrality”.

(Of course, betweenness centrality is only one way to measure importance -there is no “general”/absolute way)