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I have weighted networks where weights are cosine similarities values: they are computed in function of nodes' degrees and the intersection of common neighbours.

Suppose this object is a model to describe similarity between documents from crowd-sourced database.

Now, I would like to explore the distribution of weights that nodes' neighbours have, and analyse if there are differences of distributions for different nodes and analyse if and how the distributions of nodes may change as long as the weighted network evolves in time.

What kind of model(s) may I choose and expect? Are there any theoretical reference ?

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