I'm looking for the way to increase tezos-node connectivity. It seems that the best way is to increase number of peers (or maybe their quality somehow?).
So the question is - how should I configure
config.json in order to have optimal number of peers connected to my node?
On your side, a first step would be to set
--connections option to eg. 1000 or 10000 (assuming you have enough resources for that. I remember there was an issue with the number of opened file descriptors in the past that makes the node crash, and attempting to establish too may connection could trigger the issue.).
Then, if you can initialize your node with a "good set of peers" (both in number of peers an in quality), this would also help. For instance, you can copy the running peers shown by tzscan (https://tzscan.io/network) as a starting point.
Note that, a connection to another node can be refused for several reasons: your node has been blacklisted for some reason, the other node considers that it has enough connections, the other peer is not connected at all, ...