Dynamical topology of highly aggregated input–output networks

Abstract The paper studies topological properties of weighted directed graphs corresponding to highly aggregated macroeconomic input–output networks in Russia and the USA. As these graphs are complete or almost complete the study focuses on weight-sensitive characteristics of weighted directed networks. The analysis shows that while some generic features such as the fat-tailed nature of edge weight distribution, weighted fraction of triangles of different types and, to a certain extent, ranking with respect to PageRank and Hubs centrality are universal and do not change in time, the slopes of edge weight distributions, values of clustering coefficients and ranking of vertices with respect to certain centrality measures show visible evolution. The evolution of input–output matrices is also studied through analyzing the evolution of a distance between input–output matrices at varying time horizons.