That is the new "home" they rolled out like two years ago. There is still a setting which lets you only have a predictable and managed feed, and assuming you block ads you have a decent experience with only tweets or retweets from people you follow.

What's so strange is that I don't even recognise this description of twitter, and I've been using it for many years. My feed is almost entirely tweets from people I follow, with the occasional ad. I don't even understand what you mean by "network" as distinct from the people you follow. Can I ask, if you can recall, how many people you followed? It's possible that there's a minimum threshold to avoid noise.

I only followed a couple hundred people.

I'm following 700 and it's generally a positive experience. I think, as other have pointed out, it could be the 'hot'/latest switch which, I fully agree, is an issue.

The trick is never to look at the main feed.

Create lists of people (just one if you want the main feed-like experience, several if you want some order and structure). Only look at those lists.

They are chronological, and without the random "suggestions" Twitter likes to put before you.

And then you may come to like tweetdeck.twitter.com, where you can see all those lists side by side, and even have sensible keyboard shortcuts.

(Unfortunately, Tweetdeck may become a paid feature, there have been rumors bout it for quite some time)

in the top right of the timeline there's a button whose icon looks like a few sparkles. Hit that and switch your feed from "Home" to "Latest Tweets" and you'll only ever see tweets form people you follow, listed chronologically.