Earlier, it was possible to see how big is your network (like cca 10,000 people up to 3rd degree). Now, I am not able to get this information. Is it somehow possible?
The LinkedIn Network Statistics Link will give you an estimate of your first, second and third degree connections laid out like so:
LinkedIn no longer officially supports network statistics, and according to this article the statistics themselves were never accurate, per se (evidence includes network sizes precipitously dropping, and second and third degree connections decreasing with the addition of first degree connections).
This article, How to Find Your LinkedIn Network Statistics also gives alternatives for finding, estimating and visualizing your network size.
If you enter an asterisk into the search bar which will give you the number of results through which you are searching in your network.
This will also return your number of second degree connections, displayed further down the left-hand navigation bar: