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The function of VLAN Trunking Protocol (VTP) is to centralize VLAN management across switches within a network. By using VTP, network administrators can create, delete, and modify VLANs in one location, and these changes propagate automatically to all switches in the same VTP domain. This ensures consistency and reduces the potential for configuration errors that could arise if each switch were managed individually.

VTP operates by advertising VLAN information over trunk links, which allows switches to maintain an accurate and synchronized VLAN database. This simplification of VLAN management is particularly beneficial in larger networks where numerous switches and VLANs are used.

In contrast, the other options refer to different network functions: managing IP addressing pertains to protocols like DHCP; tracking network performance metrics would involve network monitoring tools; and encrypting data traffic on VLANs is handled through security protocols rather than VTP. Thus, the centralization of VLAN management is indeed the core purpose of VTP in a network.