Final answer:
The places where participants of a criminal network congregate, often known as 'hangouts', are referred to by terms such as 'vice districts' or 'tenderloin districts'. These areas are known for illegal activities and historically have seen collusion between law enforcement and vice establishments.
Step-by-step explanation:
The places where participants of a criminal network congregate, often referred to as "hangouts", are known by various names depending on their function and nature. These might include 'red-light districts', 'vice districts', 'brothels', and 'underground empires' among others. In many instances, these locations operate with a level of impunity due to collusion between vice establishments and law enforcement, where bribes and the pretense of enforcement create a tolerated space for illegal activities.
In the context of the provided texts, these places might most aptly be referred to as vice districts. This term describes areas where illegal activities such as prostitution, gambling, and the sale of illicit goods are concentrated and are repeatedly mentioned in historical accounts and discussions on criminal networks and their geographies.
A 'tenderloin district' is another term that historically denotes an area within a city known for its vice-related activities. For example, 'Madame' Chambers from Kansas City used her influence in the police department to protect the identity of clients attending her brothel, which was a part of the city's tenderloin district, indicating the linked relationship between crime and vice districts. This collusion between law enforcement and criminal activities in such districts is a recurrent theme in history.