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Unfortunately, there is no standard and accurate academic definition for Darknet(not dark web ,deep web, although there is not standard and accurate academic definition).

Mostly the Wikipedia's definition is referenced.

if you have a standard and accurate standard, I would be grateful?

But my main vagueness is the definition of Wikipedia which says:

A darknet (or dark net) is an overlay network that can only be accessed with specific software, configurations, or authorization, often using non-standard communications protocols and ports.

what does "non-standard communications protocols and ports" means? are not Tor , I2p , Freenet ,... standard protocols?

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I think (maybe) it means they don't use standard Internet protocols to provide the same Internet services.
For example, when you go to https://tor.stackexchange.com/, your browser sends a DNS request to your default DNS server, sends a TCP SYN packet (make a connection) to the address it resolves to, and sends a HTTP request over the connection. When you go to http://anyhiddenservice.onion/, your browser asks onion proxy to connect to that HS (if no DNS leaks), onion proxy does all complicated work (initiate a lookup, build circuits, make a stream aka. connection, etc. These are in Tor's non-standard protocol), and your browser just sends (nearly) the same HTTP request over Tor. Note that Tor works on Transport Layer, so things on the top of transport still remain interoperable with standard protocols (yes, HTTP).

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