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Network analysis has been applied to various correlation matrix data.Thresholding on the value of the pairwise correlation is probably the moststraightforward and common method to create a network from a correlationmatrix. However, there have been criticisms on this thresholding approach suchas an inability to filter out spurious correlations, which have led toproposals of alternative methods to overcome some of the problems. We propose amethod to create networks from correlation matrices based on optimisation withregularization, where we lay an edge between each pair of nodes if and only ifthe edge is unexpected from a null model. The proposed algorithm isadvantageous in that it can be combined with different types of null models.Moreover, the algorithm can select the most plausible null model from a set ofcandidate null models using a model selection criterion. For three economicdata sets, we find that the configuration model for correlation matrices isoften preferred to standard null models. For country-level product export data,the present method better predicts main products exported from countries thansample correlation matrices do.

Constructing networks by filtering correlation matrices: A null model approach