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The protocol classified as an exterior gateway protocol used by private networks is EGP. Exterior Gateway Protocols (EGPs) are designed for routing between autonomous systems, which are collections of IP networks and routers under the control of a single organization. EGP enables various networks to communicate beyond their own boundaries, facilitating the exchange of routing information between different administrative domains.

In contrast, the other protocols listed are primarily classified as interior gateway protocols, which are intended for routing within a single autonomous system. IGRP (Interior Gateway Routing Protocol) and EIGRP (Enhanced Interior Gateway Routing Protocol) are both developed by Cisco for routing within a network and are specifically designed for efficiency and adaptability in environments managed by a single organization. OSPF (Open Shortest Path First) is also an interior gateway protocol that is used extensively in large enterprise networks to manage routing within a single organization but does not function as an exterior gateway protocol.