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Similarity networks
In similarity networks, connections are less literal and more abstract. Edge weights correspond to how similar two nodes are, often with zero being not at all, and one being identical. For example, one type of similarity between different people could be calculated by taking their top-10 favorite online cat videos and using the fraction of videos that appear for both people. In this case, the edge weight doesn't have anything to do with whether two people have any kind of relationship. It's quite possible to have an edge with a very high weight connecting two individuals who have never even met!