Testing “efficient supply chain propositions” using topological characterization of the global supply chain network

In this paper, we study the topological properties of the global supply chain network in terms of its degree distribution, clustering coefficient, degree-degree correlation, bow-tie structure, and community structure to test the efficient supply chain propositions proposed by E. J.S. Hearnshaw et al. The global supply chain data in the year 2017 are constructed by collecting various company data from the web site of Standard & Poor’s Capital IQ platform. The in- and out-degree distributions are characterized by a power law of the form of γin = 2.42 and γout = 2.11. The clustering coefficient decays 〈C(k)〉∼k-βk with an exponent βk = 0.46. The nodal degree-degree correlations 〈knn(k)〉 indicates the absence of assortativity. The bow-tie structure of giant weakly connected component (GWCC) reveals that the OUT component is the largest and consists 41.1% of all firms. The giant strong connected component (GSCC) is comprised of 16.4% of all firms. We observe that upstream or downstream firms are located a few steps away from the GSCC. Furthermore, we uncover the community structures of the network and characterize them according to their location and industry classification. We observe that the largest community consists of the consumer discretionary sector based mainly in the United States (US). These firms belong to the OUT component in the bow-tie structure of the global supply chain network. Finally, we confirm the validity of Hearnshaw et al.’s efficient supply chain propositions, namely Proposition S1 (short path length), Proposition S2 (power-law degree distribution), Proposition S3 (high clustering coefficient), Proposition S4 (“fit-gets-richer” growth mechanism), Proposition S5 (truncation of power-law degree distribution), and Proposition S7 (community structure with overlapping boundaries) regarding the global supply chain network. While the original propositions S1 just mentioned a short path length, we found the short path from the GSCC to IN and OUT by analyzing the bow-tie structure. Therefore, the short path length in the bow-tie structure is a conceptual addition to the original propositions of Hearnshaw.

We added the sentence, "The vertical axis is aggregated for firms of each country in the global supply chain data." to the caption of Fig. 1.
Comment #1-2 11.-12. In line 216 the Authors draw attention to a difference between their results and previous ones. There should be a discussion of this difference. Similarly, in line 220 there is a difference revealed with respect to many other networks. There should be a discussion about the reasons of this difference.
• Still I feel that some discussion is missing, or at least clarifying the reasons why this discussion is not given here.
Response to the comment: line 278-283 in the revised paper We added the following explanation for the small SCC in the global supply chain network.
In Japan, there is a large SCC in the ownership network [1]. This is well known as crossshareholding, or "keiretsu" (a set of companies with interlocking business relationships and shareholdings) in Japanese. Correspondingly, there is a large SCC in the Japanese supply chain. On the other hand, the cross-shareholdings are not as pronounced in the world's firms as in Japan. As a result, the SCC is small in the global supply chain network.
[ • This should be indicated in the text as well.
Response to the comment: Propositions S3: However, the value of the clustering coefficient is not too high (<<1). The observed moderate clustering coefficient indicates that Proposition S3: It has a high clustering coefficient. is weakly valid.
We changed these sentences in line 410-413 in the revised paper to as follows.
However, the value of the clustering coefficient is equivalent to many other networks, such as the power grid, mobile phone calls, science collaboration, etc. The observed moderate clustering coefficient indicates that Proposition S3: It has a high clustering coefficient. is valid.
Reviewer #2: I think the authors have improved the quality of the manuscript by clarifying the aim of the paper. However, I have few remarks: -the network is directed as the authors affirm, but the authors decided to apply some topological indicators using the directed network, while others have been applied using an undirected network. I think this choice must be justified. For instance, this is the case of community detection and clustering.
Response to the comment: We have used an undirected version of the network for measuring the clustering coefficient and average nearest neighbor degree to show the presence of hierarchical structure and degree mixing property of the network as the basic structural properties. Reviewer #3: Most points have been addressed by the authors, and the manuscript has a much clearer argumentation. However, one main concern that I had with the first version of the manuscript is still not sufficiently addressed.

Comment #3-1
This main concern is the lack of conceptual integration of the two major ambitions of the the ambiguous language of "verifying". While I recognize that there are multiple methodological traditions in science, I would believe that there is the broadest agreement that "verification" is never possible in the empirical sciences, and we should think about "testing" instead. A theory will never be verified, but rather tested, and found support for. I would strongly urge the authors to re-phrase "verification" for testing, with an indication of what aspects of the theory from Hearnshaw et al. they found support for.
This could help clarify the contribution of the manuscript as well. If I was the author, I would explore ways in which the novelty of the contribution can be identified, and highlighted already in the abstract.
Response to the comment: I appreciate the excellent suggestion. I agree to re-phrase "verification" for "testing." However, to my knowledge, in the natural sciences, the word "verify" is sometimes used in the same sense as "test." For example, "experimental verification" is found in many literature.
We added the following sentences after Line 383 in the revised paper and changed the abstract and conclusions.
Original propositions of Hearnshaw S1 just mentioned a short characteristics path length. As described in the discussion of Table 4, the upstream or downstream firms are located only a few steps away from the GSCC. The short path from the GSCC to IN and OUT was only discovered by analyzing the bow-tie structure. Therefore, the short path length in the bow-tie structure is a conceptual addition to the original propositions of Hearnshaw.

Comment #3-2
As a more minor point, the network overexpression graphs for the country and industry level are much more readable, but their integration into the ambitions of the manuscript is still not clear. What aspect of Hearnshaw et al. do these talk to? I would not include almost two full page graphs that are part of only a sideline discussion, receiving only a passing mention in the text.
Response to the comment: We added the following sentences in Line 455-463 in the revised paper.
The over-expression of countries and sectors in the large communities shown in Table 5 allows us to characterize community formation by two factors. One is the over-expression of countries in the large communities shown in Fig. 6. The other is the over-expression network of sectors shown in Figure 7. In these figures, a country tends to form communities in neighboring countries, and a sector tends to form communities in the same industry. This result suggests that community formation is due to multiple factors, and the over-expression networks in Fig.6 and Fig.7 provide support for the appropriateness of the overlapping boundary of community formation in Proposition S7.