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We present a method for simultaneous Bayesian learning of the correlationmatrix and graphical model of a multivariate dataset, along with uncertaintiesin each, to subsequently compute distance between the learnt graphical modelsof a pair of datasets, using a new metric that approximates anuncertainty-normalised Hellinger distance between the posterior probabilitiesof the graphical models given the respective dataset; correlation between thepair of datasets is then computed as a corresponding affinity measure. Weachieve a closed-form likelihood of the between-columns correlation matrix bymarginalising over the between-row matrices. This between-columns correlationis updated first, given the data, and the graph is then updated, given thepartial correlation matrix that is computed given the updated correlation,allowing for learning of the 95$\%$ Highest Probability Density credibleregions of the correlation matrix and graphical model of the data. Differencemade to the learnt graphical model, by acknowledgement of measurement noise, isdemonstrated on a small simulated dataset, while the large humandisease-symptom network--with $>8,000$ nodes--is learnt using real data. Dataon vino-chemical attributes of Portuguese red and white wine samples areemployed to learn with-uncertainty graphical model of each dataset, andsubsequently, the distance between these learnt graphical models.

Correlation between Multivariate Datasets, from Inter-Graph Distance computed using Graphical Models Learnt With Uncertainties