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Google's John Mueller was answering questions around an old topic of Google showing only a sample of links in the link report in Google Search Console at Reddit. He said that generally if the links are not shown in the tool then they are "pretty irrelevant overall."
He did add a caveat to that saying "The exception that I can think of is if we show you a bunch of paid links that you obviously had added, and the webspam team takes a look at the situation, then they may encourage you to clean up all of the obvious paid links, including those not explicitly listed in Search Console. (For example, if you have site-wide paid links from a site, we're not going to list every URL on that site, but you should still take care of it across the whole site, either by having the paid link removed, or by disavowing the whole domain.)"
But when he was asked "So is it possible that links can negatively affect you even if they're not listed on GSC?" He responded "In general, if our systems don't even show them there, then they're pretty irrelevant overall."
Again, this topic and the debate around how could Google not show us all the links pointing to our site espesially the ones that are harming our site, is an old topic. But hey - Google thinks they do give enough data and there are third party tools for a reason.
Forum discussion at Reddit.
