Vertex centralities in input-output networks reveal the structure of modern economies

Abstract

Input-output tables describe the flows of goods and services between the sectors of an economy. These tables can be interpreted as weighted directed networks. At the usual level of aggregation, they contain nodes with strong self-loops and are almost completely connected. We derive two measures of node centrality that are well suited for such networks. Both are based on random walks and have interpretations as the propagation of supply shocks through the economy. Random walk centrality reveals the vertices most immediately affected by a shock. Counting betweenness identifies the nodes where a shock lingers longest. The two measures differ in how they treat self-loops. We apply both to data from a wide set of countries and uncover salient characteristics of the structures of these national economies. We further validate our indices by clustering according to sectors' centralities. This analysis reveals geographical proximity and similar developmental status.

Input-Output-Based Measures of Systemic Importance

“…An early attempt taking input-output as the starting point can be found in Olsen (1992). More recently McNerney (2009) studies the network properties of input-output models, while Blöchl et al (2011) use centrality measures and clustering techniques to uncover salient structural features of economies based on an interpretation of input-output tables as weighted, directed graphs. Acemoglu et al (2012) combine network theory with input-output data to study to what extent idiosyncratic sectoral shocks can affect aggregate business cycle fluctuations.…”

Flow distances on open flow networks

“…And because 2, 3, 5 are in the same cycle 2 → 5 → 3 and 2 → 4 → 5 → 3, they have the same values of t jj . Next, we compare our first-passage flow distance l ij with shortest path distance and first-passage distance based on random walks [41] on the closed version of the same network. In the latter comparison, "source" and "sink" are excluded so that the network is closed.…”

“…Both the shortest path distance [38], resistance distance [39] and the mean first-passage distance of a random walker [40][41][42][43] can reflect the intrinsic properties of the graph. However, conventional first-passage distance on a graph is based on the basic assumption that the whole network is closed, which means the random walker cannot escape from the network, thus the total number of walkers on the graph is conservative.…”

A Study on Strategic Industry Selection by Analysis of Inter-industry Network: The Case of Korea

“…F. Cerina et al [12] reported that network-based measures such as community coreness and PageRank centrality are more helpful in identifying key industries than traditional inter-industry analysis methods such as backward linkages. F. Blochl et al pointed out the limitations of traditional centralities and suggested the random walking centrality and the counting betweenness [11]. They reported that the measures are suitable to find the most immediately affected industry and the longest affected industry, respectively.…”