Distributions of Centrality measures:

Since the different centrality measures have different ranges and distribution shapes, we thought it would be more helpful to list the rankings of those centrality measures on individual people's and podcast's pages, rather than give the raw score and force the reader to come to this page to see how that score compares with other's scores. Still, it is usefull and interesting to view the different distribution shapes to help the reader understand what is being communicated by the various centrality measures. We also include the two Podcast Leader Score distributions.


Pagerank Histogram:

The pagerank score must be computed from a directed network, that is, where links point one way. The directed network for this podcast dataset has guests pointing at hosts of podcasts they have been on. Therefore, only hosts get non-zero pagerank scores, and this figure shows the distribution of hosts' pagerank scores. There is a wide range of pagerank scores, with the top two, Joe Rogan and Duncan Trussell, skewing the distribution. The best way to view the distribution, therefore, was to put the x-axis of pagerank scores on a logarithmic scale.

pr_histogram


Authority Score Histogram:

The Authority and Hub scores are computed together by the HITS algorithm, and uses the same directed network as does the pagerank score computation. Since nodes with high authority scores are defined to be those that are pointed to by nodes with high hub scores, and only hosts get "pointed at", all non-hosts get authority scores of zero, and so only hosts are shown in this distribution. The two at the top of this distribution are Cameron Esposito and Rhea Butcher, who together co-host the comedy podcast Put Your Hands Together with Cam and Rhea, which has had almost 500 different guests and releases a new episode roughly every two days.

auths_histogram


Hub Score Histogram:

The hubs scores include all people in the network. There is both a wide range of hub scores and a wide range in the frequency of ranges of hub scores, so the easiest way to view the distribution is on a log-log histogram. The low hub scores are populated by hosts who have not been guests on any podcast, such as Marshall Poe and Ethan Klein, and guests who have only been on one small podcast. The one spike above 1000 is due to guests who have only been on one of Marshall Poe's podcasts where he has on authors of various genres of books. The two people with the highest hub scores are Moshe Kasher and Pete Holmes.

hubs_histogram


Closeness Centrality Histogram:

The closeness centrality has a mostly normal looking distribution (a peak in the center with roughly equal tails). The peak above 1400 is due to guests who have only been on one of Marshall Poe's podcasts, just as in the hub scores above.

close_histogram


Degree Centrality Histogram:

Due to the wide range of degrees and frequencies of degrees, this distribution is best viewed on a log-log plot. When we do so, we see some clear structure. The left side shows a clear power-law distribution made up of guests. That power law is broken, however, on the right side where there is a clump of people at very high degree. This clump is largely made up of podcast hosts, who have a clearly separate distribution of degrees.

degree_histogram


Betweenness Centrality Histogram:

Similar to the degree centrality distribution, the betweenness centrality distribution is best viewed in log-log, but the structure is less clear. The hosts have high betweenness centrality and so are clustered on the right, but there are many guests who have been on several podcasts and have similarly high betweenness centrality, so those two clumps are somewhat overlapping. At the low end there are plenty of guests who have only been on one or a few podcasts.

bt_histogram


Leadership Scores Histogram:

I wanted a way to determine which podcasts were the most influential on other podcasts. That is, which are the podcasts that are first to have on certain popular guests. I measured this popularity in two ways: one was just the current hub score, a measure of current popularity; the other was the change in betweenness centrality from 2017 to 2018, a measure of increase in popularity and diversity of podcasts on which they appear. The majority of podcasts have a score of zero for both measures. The outlier with the Hub Leadership score above 8 is Put Your Hands Together with Cam and Rhea, and the two highest New Leadership scorers are New Books in Biography and The Joe Rogan Experience.

leader_hist