A system and method for facilitating connecting a switch to a network to improve network performance. In an illustrative embodiment, the system includes a first module for determining when the switch is initially connected to a network and providing a signal in response thereto. A second module selectively forms adjacencies with peers of the switch in response to the signal and based on one or more predetermined parameters. In a more specific embodiment, the switch is a router or Layer-3 (L3) switch. The one or more predetermined parameters include a load factor, values pertaining to capabilities of a processor included in the router, bandwidth capabilities of the interface and/or the router, internal router queue counts, and so on. The router employs a routing protocol such as Enhanced Interior Gateway Routing Protocol (EIGRP). The second module throttles and adjacency-formation rate based on the predetermined parameters.