$p=2.13 \times 10^{-324}$ for SPMNs). Results for out-strength Laplacian spectra showed similar trends.[]{data-label="fig:laplacian-approximation-nonsimple-sortings"}](fig2-b.pdf "fig:"){width="44.00000%"}
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    (a) DPMN                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    (b) SPMN

  ![Examples of in-strength Laplacian spectra of (a) a nonsimple DPMN and (b) a nonsimple SPMN, each approximated using the same methods as described in Section \[sec:simple\] [@sayama2016estimation] (black dashed curves), in comparison with the actual ones (gray solid curves). Eigenvalues are sorted by their real parts in an ascending order, and only their real parts are plotted (while imaginary parts were more or less randomly distributed). Two adjacency matrices of factor networks used were: $A_G=$ a $50 \times 50$ random matrix whose entries were randomly sampled from a uniform distribution $[-1,1]$, and $A_H=$ a $30          ![Examples of in-strength Laplacian spectra of (a) a nonsimple DPMN and (b) a nonsimple SPMN, each approximated using the same methods as described in Section \[sec:simple\] [@sayama2016estimation] (black dashed curves), in comparison with the actual ones (gray solid curves). Eigenvalues are sorted by their real parts in an ascending order, and only their real parts are plotted (while imaginary parts were more or less randomly distributed). Two adjacency matrices of factor networks used were: $A_G=$ a $50 \times 50$ random matrix 