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Correlation matrices are a major type of multivariate data. To examineproperties of a given correlation matrix, a common practice is to compare thesame quantity between the original correlation matrix and reference correlationmatrices, such as those derived from random matrix theory, that partiallypreserve properties of the original matrix. We propose a model to generate suchreference correlation and covariance matrices for the given matrix. Correlationmatrices are often analysed as networks, which are heterogeneous across nodesin terms of the total connectivity to other nodes for each node. Given thisbackground, the present algorithm generates random networks that preserve theexpectation of total connectivity of each node to other nodes, akin toconfiguration models for conventional networks. Our algorithm is derived fromthe maximum entropy principle. We will apply the proposed algorithm tomeasurement of clustering coefficients and community detection, both of whichrequire a null model to assess the statistical significance of the obtainedresults.

Configuration model for correlation matrices preserving the node strength