Well, like I said, the network definition is really abstract; it exists only in what you think it is, not in any one configuration file. However, if there was to be a single point of definition, it would have to be the router's configuration, as all traffic except local traffic has to go through the router. Of course, it's just as possible for the router's configuration to be incorrect as it is for any other computer's configuration to be incorrect, but the router being incorrect would affect all the other computers on the network, while any other computer being wrong would affect only the individual computer.

But, yes, you can infer the network from a (correct) IP address along with its netmask. However, something that isn't immediately obvious to practical beginners is that a network can contain more or fewer IP addresses than just the 256 defined by changing the final number. If the netmask is bigger, the network will be smaller, and vice versa. A 255.255.255.0 netmask, which is the most common netmask that novices will encounter, implies that the network is the first three numbers static, with the last number running from 0 to 255, so it's easy to infer that a computer with that netmask has a network that is the first three numbers of its IP address followed by a zero. (The network is traditionally referred to be the lowest number in the sequence, which is unusable by a computer on the network.) If the netmask were, for example, 255.255.255.240, that would imply a network with only 16 IP addresses, and if a computer in that network had an IP address of 192.168.5.67, the network's range would be 192.168.5.64-79, with the network being named 192.168.5.64. On the other hand, if the netmask were 255.255.240.0, that would be a network of 4096 IP addresses, and the same IP address would imply a range of 192.168.0.0 through 192.168.15.255.

Confused yet?