Hi Gabrielle,
From what I know, there is no a simple way to measure how close are two clusters. As it refers also to what is for you to be close.
When producing network maps in CorText Manager a maps_output.zip is produced. In one of the folder:

• maps > maps_export_format > gexf
• a file is named hhn (and not hn which contains the entire network), where you have a meta view of self-links of each clusters, and interlinks between clusters;
• the weights field for edges will help you to better understand how linked are the clusters.

You can open this file in Gephi and compute some other calculations.
  
I hope it helps
L