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I have a weighted graph as my data and lots of random graphs with the same size that are generated with uniform distribution over edges, I want to eliminate the edges of my graph that are random, but I don't know how to compare these graphs. I think p-value is a good way, but I only have one graph with lots of edges as input, how can I compute p-value for every single edge? Or is there any other ideas?

My problem is not link prediction. Actually, I have extra links. I have a dataset of links that are recorded with Hi-C technology, I know that some of the edges are random, but I don't know which of them. I tried to implement permutation test or calculating p-value, for this purpose I generated random graphs based on real data, but I don't know how to compare real graph and randoms.

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    What does it mean for an edge to be "random"? – 2017-02-27
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    @HenningMakholm The exact problem is this. The data is collected from a new technology and the graph is a biological graph. We know that some edges are recorded randomly, because of randomness in body. For this purpose we generate some random graph with equal edges, but don't know how to compare. – 2017-02-27
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    Do you mean in your graph, only a part of data points are the useful points, and others are random points? – 2017-02-27
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    @TimeCoder Yes, The density of my graph is very high, I need to delete random edges. Do you have any idea? – 2017-02-27
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    You can try RANSAC algorithm's idea. If you can show me your graph, I may help. I have already written some programs for kicking out the bad data points before. – 2017-02-28
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    @TimeCoder Many thanks for your reply. The data is very big and the density of graph is very high. I don't know how to show the graph to you, but I would be very grateful if you help to find out a way to decrease density and delete random edges. – 2017-02-28

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You may want to have a look to https://arxiv.org/abs/1010.0725, maybe this comes in handy http://snap.stanford.edu/mlg2013/submissions/mlg2013_submission_24.pdf

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    My problem is not link prediction. Actually, I have extra links. I have a dataset of links that are recorded with Hi-C technology, I know that some of the edges are random, but I don't know which of them. I tried to implement permutation test or calculating p-value, for this purpose I generated random graphs based on real data, but I don't know how to compare real graph and randoms. – 2017-02-27
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    yes, but sometimes link prediction is useful in your context too! Check 6.1 of my first link and its references, maybe it can help! Good luck! – 2017-02-27
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    Thanks a lot for your reply. – 2017-02-27