To best understand how blockchain-tracking software works, it helps to view Bitcoin as a kind of financial social network. The same kinds of mechanisms used to break privacy in social networks, by analyzing social network topology, can be used to break privacy in the Bitcoin network. By taking a pre-existing social network like Facebook, we can use that information to generate heuristics about who is transacting with whom on Bitcoin.
There is a relevant research paper that attempted to identify Twitter users by using data from Flickr. They took the twitter data, and stripped away all identifying information about the user such as name or username. Then, by looking at the social network topology of the anonymized twitter data and comparing it to the flickr data, they found that they could identify one third of twitter users, even though the twitter data was anonymized.
This research also applies to Bitcoin. If we take an anonymous network such as Bitcoin, and use data from a social network from Facebook or Bitcointalk, we can use topological analysis to identify a lot of users. A comprehensive study on Bitcoin’s privacy also shows that even with best practices, a significant proportion of users can be identified from their behaviour.
The converse is also true where Bitcoin’s network can also deanonymize TOR users.