In the definition of a network, are we only considering connected graphs ?
Because I keep encountering definitions that don't assume explicitly that we deal with connected graphs, but which would be very counter-intuitive if they would also apply for disconnected graphs (almost everywhere one is advised to think of a network - the mathematical object - as a network of pipes transporting some fluid; if disconnected graphs come into play this metaphor of pipes transporting something fails!).
On
It is possible that the author had a sensor network in mind. These usually have sensors (sources) and a sink that fuses the sensor readings. The capacity can also be defined.
These networks may or may not be connected. Obviously it helps if there is always a path from all sources to the sink. If the path momentarily disappears, the sources may store their readings until a route is re-established, etc.
I don't see how the metaphor fails if the graph is disconnected. Your pipe system is just broken (or perhaps under construction), and no flow is possible. A broken system of pipes is still a system of pipes.