Do we know how many nodes are connected to network?

[BlackHatCoiner]

Well we couldn't know something like that, it would be like how many IPs exist.

But, maybe we could calculate, almost, the number of nodes based on those connected to the default of bitcoin core when you're downloading it?

[Yogee]

Some of the articles that can be found over the internet says there are already over 100,000 nodes.
https://bitcoinist.com/bitcoin-network-surpasses-100000-nodes-new-data-shows/

Coindance, however, claims there are over 8K public nodes at the moment
https://coin.dance/nodes

 

[Tipstar]

This site literally shows the live number of nodes https://bitnodes.io/

I think this also does not include the listening only nodes and are just the active fully-validating nodes.
They also break it down by countries which shows US and Germany are the leaders for fully validating nodes.

[dothebeats]

Well we couldn't know something like that, it would be like how many IPs exist.

That particular information IMO is publicly available and there are websites dedicated to showing the number of active nodes which help the bitcoin network. One example is given by the user above. And this one also lists the current number of nodes for bitcoin and other cryptocurrencies.

But, maybe we could calculate, almost, the number of nodes based on those connected to the default of bitcoin core when you're downloading it?

I don't quite get what you're trying to say in here. Those peers that you see when you download bitcoin core does not represent the whole number of active bitcoin nodes.

[BlackHatCoiner]

I don't quite get what you're trying to say in here. Those peers that you see when you download bitcoin core does not represent the whole number of active bitcoin nodes.

Yes but these are the nodes that connect with most nodes of the network.

[BrewMaster]

i don't  think you have to necessarily connect to most nodes to get an estimation of the number of bitcoin nodes that could be connected to. all you have to do is run a full node and ask another node for an "addr" message which they would reply with a list of nodes they know of. repeating that from a couple of other random nodes could improve the accuracy but it is still an estimation.
to get all nodes (including nodes that could not be connected to) is a lot more complicated since they don't allow incoming connection and they have to connect to you.