amillionyears - 14:13 "turn off the entire computer network?"
I doubt there's a simple switch but there are relatively few connecting points in each country, without which the internet could become "national" only rather than international, or even more restricted.
There are a few data centres around London without which the bulk of UK citizens could not get online (as BT and others route most traffic there, and even if your ISP is based in Exeter or Sheffield, they will (generally) have equipment in London.
A US computing lecturer was banned from discussing some of his research because he identified the major switches across N America which are "key" to the internet working for the US and Canada. 7 bombs would be enough to not just 'break' the net for the USA, but many other countries too, because the majority of links are to/from USA (as most web hosting is located there and demands for traffic are higher to/from USA than most other countries (at least for the English-speaking world).
It's easy to see the links with a trace command:
Quick traces to a couple of USA web sites
C:\Users\webman>tracert www.imdb.com
Tracing route to us.dd.imdb.com [207.171.162.180]
over a maximum of 30 hops:
1 192.168.1.191
2 172.30.132.74
3 te-4-2.car1. Manchester1 .Level3.net [195.50.119.9]
4 ae-4-4.ebr1. London1 .Level3.net [4.69.133.102]
5 vlan104.ebr2. London1 .Level3.net [4.69.143.98]
6 ae-43-43.ebr1. NewYork1 .Level3.net [4.69.137.74]
7 ae-10-10.ebr2. Washington12 .Level3.net [4.69.148.50]
8 ae-5-5.ebr2. Washington1 .Level3.net [4.69.143.221]
9 ae-62-62.csw1. Washington1 .Level3.net [4.69.134.146]
...
Trace complete.
...
4 ae-4-4.ebr1.London1.Level3.net [4.69.133.102]
5 vlan104.ebr2. London1 .Level3.net [4.69.143.98]
8 ae-1-100.ebr2. NewYork2 .Level3.net [4.69.135.254]
10 ae-6-6.ebr1. Chicago2 .Level3.net [4.69.140.190]
11 ae-3-3.ebr2. Denver1 .Level3.net [4.69.132.61]
12 ae-2-2.ebr2. Seattle1 .Level3.net [4.69.132.53]
Now to AUSTRALIA ABC radio/TV service
(goes across USA)
C:\Users\webman>tracert www.abc.com.au
3 te-4-2.car1. Manchester1 .Level3.net [195.50.119.9]
...
8 ae-72-72.ebr2. NewYork1 .Level3.net [4.69.148.37]
9 4.69.135.185
10 ae-71-71.csw2. SanJose1 .Level3.net [4.69.153.6]
11 ae-12-70.car2. SanJose2 .Level3.net [4.69.152.76]
12 TELECOM-NEW.car2. SanJose2 .Level3.net [4.59.4.94]
links next to New Zealand...
13 ae0.sjbr2. global-gateway.net.nz [203.96.120.73]
14 ae1-3.labr5.global-gateway.net.nz [203.96.120.93]
...
18 aapt-int.sebr2.global-gateway.net.nz [202.50.238.214]
Then to Australia
19 te2-4.sglebdist01. aapt.net.au [202.10.14.6]
20 te2-1-110.sglebdist02. aapt.net.au [202.10.12.131]
ends up at ABC gateway
24 DABC12345-1.gw.connect.com.au [210.8.2.253]
and another, this time to Singapore
(again, goes across USA)
C:\Users\webman>
C:\Users\webman>tracert www.singaporeedu.gov.sg
Tracing route to www.singaporeedu.gov.sg [160.96.1.185]
over a maximum of 30 hops:
1 192.168.1.191
2 172.30.132.113
3 te-4-2.car1.Manchester1.Level3.net [195.50.119.9]
4 ae-4-4.ebr1.London1.Level3.net [4.69.133.102]
8 ae-92-92.ebr2.NewYork1.Level3.net [4.69.148.45]
...
12 STARHUB-LTD.edge5. SanJose1 .Level3.net [4.53.28.6]
California direct to Singapore, or so it seems...
13 vlan905-an-cat6k-ts2-r1. starhub.net.sg [203.118.3.153]
14 gi8-1-0-an-ats-loc04.starhub.net.sg [203.118.7.11]
...
So you can see that Australia/NZ would continue to see websites locally, but if San Jose link went down, might be "cut off" as far as the internet, not just from USA but perhaps bulk of the world, too.