That suggests such a small pool of people that it is a viable probability. I've worked in several different companies, all in the same field, for over 20 years and nobody at any one of them knew anybody from anywhere else. The idea that networking is of paramount importance isn't viable.
Your mileage may vary.
Of course you can get a job without contacts.
But networking makes it easier.
As I'd mentioned elsewhere....you work with people you get along with and respect. They or you move on to other jobs. I mean, these days, staying at ONE place isn't usually going to advance you $$ the way changing jobs every 3-4 years.....
Anyway, as people you know disperse...you stay in touch. Then say YOU need a job. Well, it sure is much easier to start by reaching out to friends you know to get your foot in the door.
Ask yourself, who's going to get first and likely best shot at a new position? Someone who comes in recommended, maybe even a personal introduction before an interview even comes up....and is vouched for by someone already there and trusted....or, someone who's only contact with the company is a faceless resume in a file folder in some HR desk?
I do it for folks I know...they do it for me.
Sure you can cold call, cold interview....but it sure is easier doing it through a network of people you've worked with over the years and getting that foot in the door and getting your name to the top of the list is often the difference in getting a job or not.
It can also work the OPPOSITE way...if you are someone that I've known of, that isn't competent, or who is difficult to work with...guess who the manager or hiring person is told NOT to hire, put at the bottom of the pile or in the circular file bin? Hmm?
Yeah, it pays to build networks, and it is also as important to not burn bridges or be an unsociable asshole.