If the host part of a IPv4 address is all zero (e.g. 192.168.1.0 in a network with mask 255.255.255.0), does the address represent the network, or a network interface in the network?
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For IPv4, that is the network address, and it cannot be assigned to an interface*. The network, itself, does not have an interface; it is the collection of interfaces with addressing that masks to the same network address.
That is explained in this two-part answer to which I have previously referred you.
Unlike IPv4, IPv6 actually allows the use of the network address for a host interface, and it has no broadcast, so all network addresses can be used for host addressing.
*There are two exceptions to being unable to use the network address for an interface, and those are
The host part all zero is used as the network address or prefix, e.g. 192.168.1.0/24. Interfaces within the network usually cannot have all zeros in the host part and all ones is reserved for the directed broadcast address.
(There's no strict technical reason why the all-zero address cannot be used but only very few systems support it.)