System threshold for the similarity of cosines to TF-IDF scales

I am analyzing several thousand (for example, 10,000) text documents. I calculated the weight of TF-IDF and had a matrix with similar pairwise cosines. I want to consider documents as a graph for analyzing various properties (for example, the length separating groups of documents) and visualizing connections as a network.

The problem is that there are too many similarities. Most of them are too small to be meaningful. I see that many people face this problem, dropping all similarities below a certain threshold, for example, similarities below 0.5.

However, 0.5 (or 0.6, or 0.7, etc.) is an arbitrary threshold, and I am looking for methods that are more objective or systematic to get rid of tiny similarities.

I am open to many different strategies. For example, is there another tf-idf alternative that would make most of the small similarities 0? Other methods to preserve only significant similarities?

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In short, take the average cosine of the initial clustering or even all of the initial offers and accept or reject the clusters based on something like the following.

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average(cosine_similarities)+alpha*standard_deviation(cosine_similarities)

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Xbar +/- tsub(alpha/2)*sample_std/sqrt(sample_size)

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