Iran cuts 95% of Internet traffic

The vast majority of Iranian ISPs' international transit
connectivity is through AS12880 DCI , which is a government
run telecom authority. Google "AS12880 DCI Iran" for more
info. DCI is also responsible for layer 2 transport and
DWDM services for smaller downstream ISPs, on other
international terrestrial fiber links, which are opaque to
us NANOG list people from the perspective of global v4/v6
routing table/prefix announcement analysis.

"Internet penetration and complexity has vastly grown in Iran
over the past decade, but the country’s users still connect
to the global network through just two gateways. Both are
controlled by the regime, and can be blocked when it chooses."

"Access to the internet is gradually being restored in Iran
after an unprecedented five-day shutdown that cut its population
off from the rest of the world and suppressed news of the
deadliest unrest since the country’s 1979 revolution."

Gradually? How long does it take to plug in a network connection and converge BGP?

Like most things it is a matter of motivation. A gun held to the head will change "gradually" into "instantly" ... it can also change "instantly" into "gradually over the next week" depending on the requirements of he who holds the gun.