At what point does a privately owned network connected to other privately owned networks become 'the Internet'?

My lack of political understanding coupled with a knowledge of how the 'Internet' actually exists and functions make it seem almost impossible for regulation to have any effect.

Think of the internet like the roads here in the US. Once you connect up "your" road to any of the other roads that are connected together, you can drive pretty much anywhere that also has a road.

At its core, "The Internet" is equal parts CenturyLink, Telecom Italia, Verizon, Sprint, TeliaSonera, NTT, Deutsche Telekom, Level 3, Tata, and AT&T. Following my above example, all of these companies have really big freeways that are all interconnected. If your road, or the bigger road you connected to, connects to one of these major freeways, you can be confident that you can reach any destination that also has a road. If Verizon were to disconnect its freeways from Sprint, the Internet would be "broken."

I think you misunderstand my lack of understanding. I'm very familiar with the Internet, peering (settlement free or otherwise), 'default free zone', etc.

What I'm asking is, given that there is NO public infrastructure (in the US at least, again, going back to my question), at what point does a private set of interconnected networks become 'the Internet' for regulatory and oversight purposes?

Does a large set of MPLS tunnel over a different providers networks constitute part of The Internet?

Does just the circuit path within the territory of the United States constitute the 'Internet' as far as the USG is concerned? Do we need filtering routers on every border? What happens when I peer with a different provider over a new circuit that's not connected to the current Internet? At what scale does that become 'the Internet Too'? I2, Lambda Rail, ESNet, etc. There are dozens of HUGE, international, not-the-internet networks running IP with IANA assigned address space, etc. Do these count as 'The Internet'?

When Cogent and L3 decide to have another spat and de-peer, and the world now has two congruent but unequal routing tables, without full reachability or visibility, which one is The Internet? Do we now have 2 Internets?

And back to the Public Infrastructure - does the US presume to provide rules and regulations over the national infrastructure of other countries? Many nation states have monopoly, government owned network / phone service providers - does the US really think they can dictate what those other countries do? And if the regulations only apply to stuff 'physically' in the US...well, what's physically mean in a virtualized, cloudy world?

To use your analogy - I own the property and the pavement of the roads around my house, and they are NOT public roads (ie: private development, shopping mall, etc.). The DoT doesn't enforce any law, such as speed limit, equipment condition, etc. on these types of setups - only on the Public Infrastructure. The Internet is just a bunch of these private shopping malls connected to each other - there are NO public roads (in the US at least).

Here's my take at a definition:

A privately owned network is "on the Internet" in the usual sense if it uses IPv4 (or maybe 6), is properly assigned IP addresses that are not in the private use area (publicly routable IPs), and has some systems that can exchange packets with the diversity of other networks that make up "the Internet". NAT devices tend to complicate this definition.

But that's a technical definition. You're asking about how it could be politically regulated.

Almost all privately owned networks (other than ISPs themselves) pay an "internet service provider" for "internet services". So you're not going to weasel out of regulation by nitpicking about the definition of "the Internet".