__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 w_{i}, to the fraction of that podcast's guests whose top category matches that of the first-listed category, denoted here as q_{i}. The bias, denoted here as b_{i}, is determined by the equation below, such that if q_{i}=w_{i}, then b_{i}=1, but if q_{i}>w_{i}, e.g. a 'Comedy' podcast has a higher proportion of 'Comedy' guests than the overall population, then we get b_{i}>1.

__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.

__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.