This figure represents the phonological neighborhood of the word 'log'. This phonological neighborhood consists of words that sound similar to 'log', such as 'dog', 'hog', 'loss' and 'lag'. Words that sound similar to each other are connected to each other.
If you look closely at 'My First Network' and 'My Second Network' you will realize that they have the same number of nodes! What is different is that fewer of log's 'neighbors' are also neighbors of each other. So, as compared to 'badge', the words that sound like 'log' do not tend to sound like each other, which makes for a less densely connected phonological neighborhood. Cool beans.
Again, I made this with code adapted from http://www.r-bloggers.com/the-maker-way-using-r-to-reify-social-media-data-via-3d-printing/