In mathematics, topology is the study of the properties of space that are preserved under continuous deformations.
Network topology refers to the arrangement of elements in a communication network, such as links and nodes. This most likely references how the Topologics are CyberseLink Monsters whose effects activate when linked.
"Topologic" monsters usually involve mass removal of cards whenever a monster is Special Summoned to a Zone a Link Monster points to. In addition, they inflict heavy effect damage.