The Floo Network Authority is a Ministry of Magic board that establishes, maintains, monitors, and regulates the Floo Network. Employees of the authority have the power to observe and monitor Floo Network connections, and may eavesdrop on conversations held through the Network. Such workers are known as Floo Network Regulators.
Madam Edgecombe works for the Floo Network Authority, and was party to the communications restrictions that the then - Minister for Magic, Cornelius Fudge, placed on Hogwarts School of Witchcraft and Wizardry while Dolores Umbridge was High Inquisitor, and later Headmistress of Hogwarts, Percy Weasley, as of 2014.
Monitoring Floo Conections
Because the Floo Network Authority usually monitor Floo connections they have been assigned to observe, Harry Potter, at the suggestion of Fred and George Weasley had to take advantage of this by sneaking into Umbridge's office on two separate occasions to connect to 12 Grimmauld Place, since as Umbridge mentioned to Harry earlier that the fireplace in her office was the only Floo connection in Hogwarts that was not under observation as she was also employed by the Ministry of Magic, and was highly viewed of.