Asymmetry in in-degree and out-degree distributions of large-scale industrial networks

Abstract: Many natural, physical and social networks commonly exhibit power-law degree distributions. In this paper, we discover previously unreported asymmetrical patterns in the degree distributions of incoming and outgoing links in the investigation of large-scale industrial networks, and provide interpretations. In industrial networks, nodes are firms and links are directed supplier-customer relationships. While both in- and out-degree distributions have "power law" regimes, out-degree distribution decays faster than in-degree distribution and crosses it at a consistent nodal degree. It implies that, as link degree increases, the constraints to the capacity for designing, producing and transmitting artifacts out to others grow faster than and surpasses those for acquiring, absorbing and synthesizing artifacts provided from others. We further discover that this asymmetry in decaying rates of in-degree and out-degree distributions is smaller in networks that process and transmit more decomposable artifacts, e.g. informational artifacts in contrast with physical artifacts. This asymmetry in in-degree and out-degree distributions is likely to hold for other directed networks, but to different degrees, depending on the decomposability of the processed and transmitted artifacts.