Multilayer overlaps and correlations in the bank-firm credit network of Spain

We investigate the structural dependencies in the bank-firm credit market of Spain in the year 2007 under a multilayer network perspective. In particular, we decompose the original bipartite network into different layers representing different industrial sectors. We then study the correlations between layers based on normalized measures of overlaps of links and weights of banks between layers. To assess the statistical significance of such correlations, we compare the observed values with the expected ones obtained from random graph models and so-called configuration models. While the former impose only global constraints, i.e. the total degree or the total strength in single layers, the latter preserve the intrinsic heterogeneity of the data in the form of its observed degree sequence and/or strength sequence in single layers. We find that, first, the raw dependencies between layers of the observed network are highly heterogeneous. Second, when evaluated against the null models, the rescaled correlations after filtering out the effects of the global constraints typically display no significant difference to the observed correlations. Similarly, in the binary version, almost all correlations are still present after subtracting the effects of the observed degree sequences in all layers while the observed correlations are only partially explained by the local constraints maintained in the weighted configuration models. Under all null models, we find that the multilayer credit network has a significant, non-random structure of correlations that cannot be explained by more primitive network properties alone. Disentangling the underlying contributions to the non-random elements we find that in 2007 the loan portfolios of different categories of Spanish banks (commercial and savings banks) have been very homogeneous, generating also strong overlaps in lending structure between many sectors of the economy.