RIPv2 is a distance-vector routing protocol and EIGRP is an advanced distance-vector protocol that also incorporates features of link-state protocols. Both of these protocols maintain neighbor adjacencies.

Neighbor adjacencies are maintained by exchanging hello packets between neighboring routers. These hello packets contain information about the router's identity, capabilities, and other parameters. By exchanging these hello packets, routers can establish and maintain neighbor adjacencies.

- RIPv2:
RIPv2 (Routing Information Protocol version 2) is a distance-vector routing protocol that uses hop count as its metric. It exchanges routing information between neighboring routers by sending periodic updates. When a router receives an update from a neighbor, it updates its routing table accordingly. RIPv2 also supports authentication and route summarization.

- EIGRP:
EIGRP (Enhanced Interior Gateway Routing Protocol) is an advanced distance-vector protocol that incorporates features of both distance-vector and link-state protocols. EIGRP uses a metric called "composite metric" that takes into account factors such as bandwidth, delay, reliability, and load. It also supports authentication and route summarization.

EIGRP uses hello packets for neighbor discovery and adjacency maintenance. When a router receives a hello packet from a neighbor, it checks the information in the packet and if it meets the requirements, it forms an adjacency with the neighbor. EIGRP also uses reliable transport protocol (RTP) to ensure reliable delivery of routing updates.

- Neighbor Adjacencies:
Maintaining neighbor adjacencies is crucial for routing protocols as it allows routers to exchange routing information and update their routing tables accordingly. By establishing adjacencies, routers can form a network topology and choose the best path for forwarding packets.

In conclusion, both RIPv2 and EIGRP maintain neighbor adjacencies. RIPv2 uses periodic updates to exchange routing information, while EIGRP uses hello packets and RTP for neighbor discovery and adjacency maintenance. These protocols play a vital role in building and maintaining efficient routing networks.