Pagerank:




Pagerank works by counting the number and quality of links to a node to determine a rough estimate of how important the node is. The underlying assumption is that more important nodes are likely to receive more links from other nodes. (Wikipedia page)

Hub and Authority:




Authority and hub values are defined in terms of one another in a mutual recursion via the HITS algorithm. An authority value is computed as the sum of the scaled hub values that point to that page. A hub value is the sum of the scaled authority values of the pages it points to. (Wikipedia page)

Degree Centrality:




The degree centrality for a node is the fraction of nodes it is connected to. (Wikipedia page)

Closeness Centrality:




The closeness centrality (or closeness) of a node is a measure of centrality in a network, calculated as the sum of the length of the shortest paths between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes. (Wikipedia page)

Betweenness Centrality:




The betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of nodes in a connected graph, there exists at least one shortest path between the nodes such that either the number of links that the path passes through is minimized. The betweenness centrality for each node is the number of these shortest paths that pass through the node. (Wikipedia page)

Currently Active:




A podcast is defined to be currently active if it has released an episode with 5x of the average episode frequency.

Unique Guests:




Unique guests are defined to be guests that have only appeared on that specific podcast and no others.

Top Category:




Only the podcasts have explicit categories. Each person's category is something that must be assigned. The way we do that is the following. If a person is a host, we figure out which of their podcast they've spent the most total time hosting (the sum of the durations of guest appearances) and assign to them the first-listed category of that podcast. If a person is not a host and only a guest, we figure out which podcast they've spend the most time on (again, the sum of the durations of guest appearances) and assign to them the first-listed category of that podcast.

Category Bias:




Using the distribution of top categories, for each podcast we can compare the fraction of all the people in the network whose top category matches that of the first-listed category, denoted here as wi, to the fraction of that podcast's guests whose top category matches that of the first-listed category, denoted here as qi. The bias, denoted here as bi, is determined by the equation below, such that if qi=wi, then bi=1, but if qi>wi, e.g. a 'Comedy' podcast has a higher proportion of 'Comedy' guests than the overall population, then we get bi>1.
bias equation

Density:




The density is 0 for a graph without edges and 1 for a complete graph. The value for the density is given by the equation below, where n is the number of nodes and m is the number of links in the network.
density equation

Hub Leader Score:




I wanted a measure that kept track of which podcasts were the first to have the most popular guests in the network. I calculated the hub scores of all the people, picked the top 500, then determined which podcast first had them as a guest. That podcast adds to its Hub Leader Score that person's hub score. Therefore, the podcasts that first had the guests who have the highest hub scores will be the top "Hub Podcast Leaders". I multiply this number by 100 for readability.

New Leader Score:




There are certain guests who become sudden sensations and are invited guests on several podcasts in a relatively short period of time. The best way to find these people is to track the change in their Betweenness Centrality. So I calculated the change in Betweenness Centrality from 2017 to 2018 of all the guests who are not hosts. I took the 500 guests with the biggest change in Betweenness centrality and determined which podcast first had them as a guest. That podcast adds to its New Leader Score each persons change in Betweenness centrality. I wanted a measure that kept track of which podcasts were the first to have the most popular guests in the network. I calculated the hub scores of all the people, picked the top 500, then determined which podcast first had them as a guest. That podcast adds to its Hub Leader Score that person's hub score. Therefore, the podcasts that first had the guests who have the highest hub scores will be the top "Hub Podcast Leaders". I multiply this number by 100 for readability.