Centrality PE

[@aikenong4538]

Hi, may I know what are the answers for the diameter, target for collection, and target for capture?

[@dr_smoke]

If you look at the distance matrix around 5:30 in the video, the maximum number, 3, is the diameter. I'm not sure what you mean by target for collection/capture.

[@sravanikapilavai8300]

if the sum of rows in betweenness centrality matrix should amount to one, I think path between 2,3 nodes should have 0.25 for node 1 and 5 and 0.5 to node 4.

[@jeffreyang20]

The numbers in the tutorial are correct. For Betweenness Centrality, we need to count the number of times the node was passed. Then divide by the number of shortest path for that OD pair. Node 1 was passed 1 time. Node 4 was passed 2 times. Node 5 was passed 1 time. Since there are 2 possible shortest paths. Divide the count by 2. That gives Node 1 (1/2), Node 4 (2/2), Node 5 (1/2) - as per the tutorial. I checked the same network using networkx in python. Python gives the same results as the tutorial.

[@dr_smoke]

This is not true. The numbers are the fraction of the shortest paths that the node lies on. So, for {2,3}, you'll see that node four is on both paths, so it is 1.0, but node five is on one of two paths, so it is 0.5 like node 1. In this case, the sum of the rows is 2.0.

[@aks3475]

So, Betweenness Centrality is the centrality measure that attempts to capture the centrality of a node based on the impact of connectivity of the node in a network as well the centrality measures of other nodes to which the node is connected...?

[@dr_smoke]

Not exactly. The centrality measures degree, betweenness, and closeness are all different ways of measuring what is central, much like mean, median, mode tell you what number is typical, but are slightly different. In most random networks, these three measures are all highly correlated, just like mean, median, mode in normally distributed data. When there is more structure (e.g. connected subgroups), then the measures will not be as correlated, much like mean vs median in skewed distributions. When there is structure, betweenness will measure brokerage across the groups, while degree will measure the most connected, probably in a single cluster. Closeness is somewhat in between. To follow my analogy, betweenness is like median, closeness like mean, and degree like mode.