In order to visualize connections between characters I created a force directed network graph for each book. The volumes in the Lord of the Rings was treated together to give better insight into the story.
The bubbles represent their total number of mentions across the book. In order for minor characters not to disappear completely I set both a maximum and a minimum possible size of the bubbles. The lines between two bubbles represent the total number of times both characters were mentioned on the same page.
This method for calculating character interactions is not completely optimal since characters are often mentioned on the same page even though they never meet. In the future I may develop a better approach to this. However, I believe these visualizations show interesting patterns in the narrative nonetheless. As an example the graph of Silmarillion clearly shows how big impact Melkor / Morgoth had on almost every part of the story.