Hierarchical communities in the walnut structure of the Japanese production network
Fig 7
Polarizability of the direction of links interconnecting communities at the top level.
Here, 51 major communities containing more than 1,000 firms are selected. The top figure plots the polarization ratio |Pij| of the linkage between communities i and j versus the total number Lij of its constituting links. The dashed curve shows the significance level corresponding to 2σ for the polarizability of intercommunity linkage for the given total number of its constituents, where the random orientation of the individual links is adopted as a null model; see Eq (6) for the standard deviation σ. The bottom figure is a histogram for the frequency of intercommunity linkages in each bin of Lij. The grey (black) bars depict the number of intercommunity linkages with a |Pij| that is higher (lower) than the threshold for the test of statistical significance.