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Network Analysis
807
NODES
8585
EDGES
0.875
Correct rate of friendship paradox
2.53
Average shortest path
Here is our in and out degree distribution, our network generally follows the power low, right one is log degree distribution.
Centrality
From the above 3 kinds of centrality, we can see the top-5 most important characters are always Harry, You-Know-Who, Ron, Hermione and Dumbledore, which I think are within our expection. To our surprise, we see Arthur Weasley is in No.6 of betweenness centrality. Given Arthur Weasley is a core member in Order of the Phoenix and Weasley's are always Harry's firm supporters, we think it's also reasonable. We are surprised to see Dolores Umbridge in every kind of centralities. We think that's because even though Umbridge starts to appear in the Order of Phoenix, she plays a very importance in the Order of Phoenix and the following books.
Friendship Paradox
The friendship paradox states that almost everyone has fewer friends than their friends have on average. It is because we live in a social network with a power-law degree distribution where almost everyone's friends has a hub, that drives up the average degree of the friends.
We also verify the Friendship Paradox in our network, there up to 87.5% nodes follow friendship paradox in our network.
Six Degrees of Separation
Six degrees of separation is the idea that all people are six or fewer social connections away from each other. As a result, a chain of "friend of a friend" statements can be made to connect any two people in a maximum of six steps. It is also known as the six handshakes rule.
We want to verify this interesting theory! We randomly select several characters. Let’s see start from any of them, how many steps need to be used to cover the whole network!
In bar charts of all of our selected characters, we can see that the whole network is covered within 3 steps. We further compute the average shortest path of our network, which is 2.53. Those are side verifications of six degrees of separation.
Network Visualization
House
Here is the network graph painted according to ‘house’ attribute.
We can observe that the people have no house attribute are far more than those with the house attribute. Gryffindor and Slytherin have more students mentioned in the books than the other 2 houses.
In addition, we can see that the degree of the grey nodes (no house attribute) is lower than the nodes of 4 houses. Gryffindor and Slytherin nodes have a relatively higher degree than all other nodes, considering the top-10 in 3 kinds of centrality are all Gryffindor and Slytherin people, we think it’s reasonable : )
Click on the picture to enlarge the view
Gender
Here is the network graph painted according to ‘gender’ attribute.
Our purpose to color the nodes according to genders is to check whether girls have more connection with girls, and boys have more connection with boys. From our force-directed graph, we can tell that there is no very clear tendency to make friends based on gender. From the graphs we know the number of male characters is slightly more than the number of female characters. From force-directed graph, the degree of male characters is generally higher than female characters.
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Blood
Here is the network graph painted according to ‘blood’ attribute.
Apart from the grey nodes, we can see that the pure-blood wizards account for the largest number, while muggle-born wizards account for the least number. There are many muggles, but their degree is generally smaller than all kinds of wizards. The degree of half-blood wizards are relatively higher than other kinds, after all many of our main characters Harry, Voldemort, Dumbledore... are half-blood wizards. Not surprisingly, the biggest pure-blood node is Ron and the biggest muggle-born node is Hermione.
Click on the picture to enlarge the view