and with arity has one principal port and auxiliary ports. Any port can be connected to at most one edge. Any edge is connected to exactly two ports. Ports that are not connected to any edge are called free ports. Free ports together form the interface of an interaction net. All agent types belong to a set called signature.

An interaction net that consists solely of edges is called a wiring and usually denoted as . A tree with its root is inductively defined either as an edge , or as an agent with its free principal port and its