1 Background
2 Methods
2.1 Constructing an adjacency matrix
2.2 Clustering input–output analysis
2.3 Simulation module
3 Numerical example
Clustering |
\(\text {C}_1\)
|
\(\text {C}_2\)
|
\(\text {C}_3\)
|
\(\text {C}_4\)
|
\(\text {C}_5\)
|
\(\text {C}_6\)
|
\(\text {C}_7\)
|
\(\text {C}_8\)
|
\(\text {C}_9\)
|
\(\text {C}_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(\text {Ncut}(\text {C}, \mathbf{W}_0)\)
| 1.611 | 0.556 | 0.551 | 1.09 | 1.611 | 1.412 | 0.889 | 1.791 | 1.225 | 1.412 |
Clustering |
\(\text {C}_1\)
|
\(\text {C}_2\)
|
\(\text {C}_3\)
|
\(\text {C}_4\)
|
\(\text {C}_5\)
|
\(\text {C}_6\)
|
\(\text {C}_7\)
|
\(\text {C}_8\)
|
\(\text {C}_9\)
|
\(\text {C}_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(\text {Ncut}(\text {C}, \mathbf{W}_I)\)
| 1.615 | 0.550 | 0.564 | 1.170 | 1.615 | 1.334 | 0.909 | 1.738 | 1.315 | 1.334 |
Clustering |
\(\text {C}_1\)
|
\(\text {C}_2\)
|
\(\text {C}_3\)
|
\(\text {C}_4\)
|
\(\text {C}_5\)
|
\(\text {C}_6\)
|
\(\text {C}_7\)
|
\(\text {C}_8\)
|
\(\text {C}_9\)
|
\(\text {C}_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(I_{{\mathcal {X}}}(\text {C}, \mathbf{W}_I)\)
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Performance | 2.933 | 1 | 1.024 | 2.124 | 2.933 | 2.422 | 1.651 | 3.156 | 2.387 | 2.422 |
Ratio |
Clustering |
\(\text {C}_1\)
|
\(\text {C}_2\)
|
\(\text {C}_3\)
|
\(\text {C}_4\)
|
\(\text {C}_5\)
|
\(\text {C}_6\)
|
\(\text {C}_7\)
|
\(\text {C}_8\)
|
\(\text {C}_9\)
|
\(\text {C}_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(\widehat{R_1^{\mathcal {X}}}(\text {C})\)
| 0 | 0.247 | 0.752 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
\(\widehat{R_2^{\mathcal {X}}}(\text {C})\)
| 0.333 | 0.985 | 0.996 | 0.492 | 0.333 | 0.384 | 0.611 | 0.304 | 0.443 | 0.384 |
4 Empirical results
4.1 Experiment scheme
4.2 Results and discussion
Clustering |
\(\xi =0\)
|
\(\xi =0.1\)
|
\(\xi =0.2\)
|
\(\xi =0.3\)
|
\(\xi =0.4\)
|
\(\xi =0.5\)
|
Kagawa et al. (2015) |
---|---|---|---|---|---|---|---|
Nominal Ncut | 9.800 | 11.991 | 12.931 | 12.557 | 9.521 | 9.557 | 21.564 |
Mean Ncut | 9.802 | 11.994 | 12.943 | 12.561 | 9.522 | 9.560 | 21.568 |
Clustering |
\(\xi =0\)
|
\(\xi =0.1\)
|
\(\xi =0.2\)
|
\(\xi =0.3\)
|
\(\xi =0.4\)
|
\(\xi =0.5\)
|
Kagawa et al. (2015) |
---|---|---|---|---|---|---|---|
Nominal Ncut | 9.800 | 11.991 | 12.931 | 12.557 | 9.521 | 9.557 | 21.564 |
Mean Ncut | 9.810 | 12.006 | 12.953 | 12.566 | 9.529 | 9.567 | 21.578 |
Clustering |
\(\xi =0\)
|
\(\xi =0.1\)
|
\(\xi =0.2\)
|
\(\xi =0.3\)
|
\(\xi =0.4\)
|
\(\xi =0.5\)
|
Kagawa et al. (2015) |
---|---|---|---|---|---|---|---|
Nominal Ncut | 9.800 | 11.991 | 12.931 | 12.557 | 9.521 | 9.557 | 21.564 |
Mean Ncut | 12.498 | 14.523 | 14.811 | 11.658 | 5.751 | 10.753 | 31.696 |
Rank |
Kagawa et al. (2015) | Experiment (\(\xi =0.3\)) | ||||
---|---|---|---|---|---|---|
Cluster name | Industrial sectors | Within-cluster sum | Cluster name | Industrial sectors | Within-cluster sum | |
1 | American and polonese cluster | USA: Mining and Quarrying | 49,201 | American cluster (C1) | USA: Mining and Quarrying | 164,072 |
USA: Pulp, Paper, Paper, Printing and Publishing | USA: Pulp, Paper, Paper, Printing and Publishing | |||||
USA: Coke, Refined Petroleum and Nuclear Fuel | USA: Coke, Refined Petroleum and Nuclear Fuel | |||||
USA: Chemicals and Chemical Products | USA: Chemicals and Chemical Products | |||||
USA: Rubber and Plastics | USA: Rubber and Plastics | |||||
USA: Other Non-Metallic Mineral | USA: Other Non-Metallic Mineral | |||||
USA: Basic Metals and Fabricated Metal | USA: Basic Metals and Fabricated Metal | |||||
USA: Transport Equipment | USA: Wood and Products of Wood and Cork | |||||
USA: Electricity, Gas and Water Supply | USA: Electricity, Gas and Water Supply | |||||
USA: Wholesale Trade and Commission Trade, | USA: Wholesale Trade and Commission Trade, | |||||
Except of Motor Vehicles and Motorcycles | Except of Motor Vehicles and Motorcycles | |||||
USA: Inland Transport | USA: Inland Transport | |||||
USA: Other Supporting and Auxiliary Transport | USA: Retail Trade, Except of Motor Vehicles and | |||||
Activities; Activities of Travel Agencies | Motorcycles; Repair of Household Goods | |||||
USA: Financial Intermediation | USA: Construction | |||||
USA: Renting of M&Eq and Other Business Activities | USA: Air Transport | |||||
POL: Mining and Quarrying | USA: Other Supporting and Auxiliary Transport | |||||
POL: Coke, Refined Petroleum and Nuclear Fuel | Activities; Activities of Travel Agencies | |||||
POL: Chemicals and Chemical Products | USA: Post and Telecommunications | |||||
POL: Rubber and Plastics | USA: Financial Intermediation | |||||
POL: Other Non-Metallic Mineral | USA: Renting of M&Eq and Other Business Activities | |||||
POL: Basic Metals and Fabricated Metal | USA: Other Community, Social and Personal Services | |||||
POL: Machinery, Nec | ||||||
POL: Electrical and Optical Equipment | ||||||
POL: Transport Equipment | ||||||
POL: Electricity, Gas and Water Supply | ||||||
POL: Wholesale Trade and Commission Trade, | ||||||
Except of Motor Vehicles and Motorcycles | ||||||
POL: Retail Trade, Except of Motor Vehicles and | ||||||
Motorcycles; Repair of Household Goods | ||||||
POL: Inland Transport | ||||||
POL: Real Estate Activities | ||||||
POL: Renting of M&Eq and Other Business Activities | ||||||
POL: Other Community, Social and Personal Services | ||||||
2 | Big cluster | (664 elements) | 18,488 | Chinese cluster (C2) | CHN: Agriculture, Hunting, Forestry and Fishing | 13,035 |
CHN: Mining and Quarrying | ||||||
CHN: Food, Beverages and Tobacco | ||||||
CHN: Textiles and Textile Products | ||||||
CHN: Wood and Products of Wood and Cork | ||||||
CHN: Pulp, Paper, Paper, Printing and Publishing | ||||||
CHN: Coke, Refined Petroleum and Nuclear Fuel | ||||||
CHN: Chemicals and Chemical Products | ||||||
CHN: Rubber and Plastics | ||||||
CHN: Other Non-Metallic Mineral | ||||||
CHN: Basic Metals and Fabricated Metal | ||||||
CHN: Machinery, Nec | ||||||
CHN: Electrical and Optical Equipment | ||||||
CHN: Electricity, Gas and Water Supply | ||||||
CHN: Hotels and Restaurants | ||||||
CHN: Inland Transport | ||||||
CHN: Renting of M&Eq and Other Business Activities | ||||||
3 | Chinese cluster | CHN: Agriculture, Hunting, Forestry and Fishing | 12,805 | Rest of the world cluster (C3) | DNK: Water Transport | 5963 |
CHN: Mining and Quarrying | FRA: Agriculture, Hunting, Forestry and Fishing | |||||
CHN: Food, Beverages and Tobacco | FRA: Food, Beverages and Tobacco | |||||
CHN: Textiles and Textile Products | FRA: Wood and Products of Wood and Cork | |||||
CHN: Leather, Leather and Footwear | FRA: Pulp, Paper, Paper, Printing and Publishing | |||||
CHN: Pulp, Paper, Paper, Printing and Publishing | FRA: Coke, Refined Petroleum and Nuclear Fuel | |||||
CHN: Coke, Refined Petroleum and Nuclear Fuel | FRA: Chemicals and Chemical Products | |||||
CHN: Chemicals and Chemical Products | FRA: Rubber and Plastics | |||||
CHN: Rubber and Plastics | FRA: Other Non-Metallic Mineral | |||||
CHN: Other Non-Metallic Mineral | FRA: Basic Metals and Fabricated Metal | |||||
CHN: Basic Metals and Fabricated Metal | FRA: Machinery, Nec | |||||
CHN: Machinery, Nec | FRA: Electrical and Optical Equipment | |||||
CHN: Electrical and Optical Equipment | FRA: Transport Equipment | |||||
CHN: Transport Equipment | FRA: Manufacturing, Nec; Recycling | |||||
CHN: Electricity, Gas and Water Supply | FRA: Electricity, Gas and Water Supply | |||||
CHN: Inland Transport | FRA: Sale, Maintenance and Repair of Motor Vehicles | |||||
CHN: Renting of M&Eq and Other Business Activities | and Motorcycles; Retail Sale of Fuel | |||||
FRA: Wholesale Trade and Commission Trade, | ||||||
Except of Motor Vehicles and Motorcycles | ||||||
FRA: Retail Trade, Except of Motor Vehicles and | ||||||
Motorcycles; Repair of Household Goods | ||||||
FRA: Hotels and Restaurants | ||||||
FRA: Inland Transport | ||||||
FRA: Financial Intermediation | ||||||
FRA: Renting of M&Eq and Other Business Activities | ||||||
FRA: Other Community, Social and Personal Services | ||||||
KOR: Water Transport | ||||||
ROW: Agriculture, Hunting, Forestry and Fishing | ||||||
ROW: Mining and Quarrying | ||||||
ROW: Food, Beverages and Tobacco | ||||||
ROW: Wood and Products of Wood and Cork | ||||||
ROW: Pulp, Paper, Paper, Printing and Publishing | ||||||
ROW: Chemicals and Chemical Products | ||||||
ROW: Rubber and Plastics | ||||||
ROW: Basic Metals and Fabricated Metal | ||||||
ROW: Machinery, Nec | ||||||
ROW: Electrical and Optical Equipment | ||||||
ROW: Electricity, Gas and Water Supply | ||||||
ROW: Wholesale Trade and Commission Trade, | ||||||
Except of Motor Vehicles and Motorcycles | ||||||
ROW: Retail Trade, Except of Motor Vehicles and | ||||||
Motorcycles; Repair of Household Goods | ||||||
ROW: Hotels and Restaurants | ||||||
ROW: Inland Transport | ||||||
ROW: Water Transport | ||||||
ROW: Air Transport | ||||||
ROW: Other Supporting and Auxiliary Transport | ||||||
Activities; Activities of Travel Agencies | ||||||
ROW: Post and Telecommunications | ||||||
ROW: Financial Intermediation | ||||||
ROW: Renting of M&Eq and Other Business Activities | ||||||
ROW: Other Community, Social and Personal Services | ||||||
4 | Rest of the world cluster | ROW: Mining and Quarrying | 4278 | Indian cluster (C4) | IND: Textiles and Textile Products | 1570 |
ROW: Rubber and Plastics | IND: Wood and Products of Wood and Cork | |||||
ROW: Basic Metals and Fabricated Metal | IND: Pulp, Paper, Paper, Printing and Publishing | |||||
ROW: Electricity, Gas and Water Supply | IND: Coke, Refined Petroleum and Nuclear Fuel | |||||
ROW: Inland Transport | IND: Chemicals and Chemical Products | |||||
ROW: Water Transport | IND: Rubber and Plastics | |||||
ROW: Renting of M&Eq and Other Business Activities | IND: Other Non-Metallic Mineral | |||||
IND: Basic Metals and Fabricated Metal | ||||||
IND: Machinery, Nec | ||||||
IND: Electrical and Optical Equipment | ||||||
IND: Transport Equipment | ||||||
IND: Manufacturing, Nec; Recycling | ||||||
IND: Electricity, Gas and Water Supply | ||||||
IND: Construction | ||||||
IND: Inland Transport | ||||||
IND: Post and Telecommunications | ||||||
IND: Financial Intermediation | ||||||
IND: Renting of M&Eq and Other Business Activities | ||||||
ROW: Manufacturing, Nec; Recycling | ||||||
5 | Canadian cluster | CAN: Agriculture, Hunting, Forestry and Fishing | 2110 | Mexican cluster | MEX: Agriculture, Hunting, Forestry and Fishing | 1302 |
CAN: Mining and Quarrying | MEX: Mining and Quarrying | |||||
CAN: Food, Beverages and Tobacco | MEX: Food, Beverages and Tobacco | |||||
CAN: Wood and Products of Wood and Cork | MEX: Textiles and Textile Products | |||||
CAN: Pulp, Paper, Paper, Printing and Publishing | MEX: Wood and Products of Wood and Cork | |||||
CAN: Coke, Refined Petroleum and Nuclear Fuel | MEX: Pulp, Paper, Paper, Printing and Publishing | |||||
CAN: Chemicals and Chemical Products | MEX: Coke, Refined Petroleum and Nuclear Fuel | |||||
CAN: Rubber and Plastics | MEX: Chemicals and Chemical Products | |||||
CAN: Other Non-Metallic Mineral | MEX: Rubber and Plastics | |||||
CAN: Basic Metals and Fabricated Metal | MEX: Other Non-Metallic Mineral | |||||
CAN: Machinery, Nec | MEX: Basic Metals and Fabricated Metal | |||||
CAN: Electrical and Optical Equipment | MEX: Machinery, Nec | |||||
CAN: Transport Equipment | MEX: Electrical and Optical Equipment | |||||
CAN: Electricity, Gas and Water Supply | MEX: Transport Equipment | |||||
CAN: Wholesale Trade and Commission Trade, | MEX: Wholesale Trade and Commission Trade, | |||||
Except of Motor Vehicles and Motorcycles | Except of Motor Vehicles and Motorcycles | |||||
CAN: Retail Trade, Except of Motor Vehicles and | MEX: Retail Trade, Except of Motor Vehicles and | |||||
Motorcycles; Repair of Household Goods | Motorcycles; Repair of Household Goods | |||||
CAN: Inland Transport | MEX: Inland Transport | |||||
CAN: Water Transport | MEX: Manufacturing, Nec; Recycling | |||||
CAN: Air Transport | MEX: Electricity, Gas and Water Supply | |||||
CAN: Other Supporting and Auxiliary Transport | MEX: Hotels and Restaurants | |||||
Activities; Activities of Travel Agencies | MEX: Sale, Maintenance and Repair of Motor | |||||
CAN: Post and Telecommunications | Vehicles and Motorcycles; Retail Sale of Fuel | |||||
CAN: Financial Intermediation | MEX: Financial Intermediation | |||||
CAN: Real Estate Activities | MEX: Renting of M&Eq and Other Business Activities | |||||
CAN: Renting of M&Eq and Other Business Activities | ||||||
CAN: Other Community, Social and Personal Services |
Rank |
Kagawa et al. (2015) | Experiment (\(\xi =0.4\)) | ||||
---|---|---|---|---|---|---|
Cluster name | Industrial sectors | Within-cluster sum | Cluster name | Industrial sectors | Within-cluster sum | |
1 | American cluster (1) | USA: Mining and Quarrying | 120,033 | American cluster (C5) | USA: Mining and Quarrying | 162,275 |
USA: Coke, Refined Petroleum and Nuclear Fuel | USA: Coke, Refined Petroleum and Nuclear Fuel | |||||
USA: Other Non-Metallic Mineral | USA: Other Non-Metallic Mineral | |||||
USA: Basic Metals and Fabricated Metal | USA: Basic Metals and Fabricated Metal | |||||
USA: Electricity, Gas and Water Supply | USA: Electricity, Gas and Water Supply | |||||
USA: Construction | USA: Construction | |||||
USA: Inland Transport | USA: Inland Transport | |||||
USA: Wood and Products of Wood and Cork | ||||||
USA: Pulp, Paper, Paper, Printing and Publishing | ||||||
USA: Chemicals and Chemical Products | ||||||
USA: Rubber and Plastics | ||||||
USA: Wholesale Trade and Commission Trade, | ||||||
Except of Motor Vehicles and Motorcycles | ||||||
USA: Retail Trade, Except of Motor Vehicles and | ||||||
Motorcycles; Repair of Household Goods | ||||||
USA: Air Transport | ||||||
USA: Other Supporting and Auxiliary Transport | ||||||
Activities; Activities of Travel Agencies | ||||||
USA: Financial Intermediation | ||||||
USA: Renting of M&Eq and Other Business Activities | ||||||
USA: Other Community, Social and Personal Services | ||||||
2 | Chinese cluster | CHN: Agriculture, Hunting, Forestry and Fishing | 12,900 | Chinese cluster (C6) | CHN: Agriculture, Hunting, Forestry and Fishing | 13,037 |
CHN: Mining and Quarrying | CHN: Mining and Quarrying | |||||
CHN: Food, Beverages and Tobacco | CHN: Food, Beverages and Tobacco | |||||
CHN: Textiles and Textile Products | CHN: Textiles and Textile Products | |||||
CHN: Wood and Products of Wood and Cork | CHN: Wood and Products of Wood and Cork | |||||
CHN: Pulp, Paper, Paper, Printing and Publishing | CHN: Pulp, Paper, Paper, Printing and Publishing | |||||
CHN: Coke, Refined Petroleum and Nuclear Fuel | CHN: Coke, Refined Petroleum and Nuclear Fuel | |||||
CHN: Chemicals and Chemical Products | CHN: Chemicals and Chemical Products | |||||
CHN: Rubber and Plastics | CHN: Rubber and Plastics | |||||
CHN: Other Non-Metallic Mineral | CHN: Other Non-Metallic Mineral | |||||
CHN: Basic Metals and Fabricated Metal | CHN: Basic Metals and Fabricated Metal | |||||
CHN: Machinery, Nec | CHN: Machinery, Nec | |||||
CHN: Electrical and Optical Equipment | CHN: Electrical and Optical Equipment | |||||
CHN: Electricity, Gas and Water Supply | CHN: Electricity, Gas and Water Supply | |||||
CHN: Inland Transport | CHN: Inland Transport | |||||
CHN: Renting of M&Eq and Other Business Activities | CHN: Renting of M&Eq and Other Business Activities | |||||
CHN: Hotels and Restaurants | ||||||
KOR: Agriculture, Hunting, Forestry and Fishing | ||||||
KOR: Food, Beverages and Tobacco | ||||||
3 | American cluster (2) | USA: Agriculture, Hunting, Forestry and Fishing | 7458 | Big cluster (C8) | (570 elements) | 3816 |
USA: Food, Beverages and Tobacco | ||||||
USA: Textiles and Textile Products | ||||||
USA: Wood and Products of Wood and Cork | ||||||
USA: Pulp, Paper, Paper, Printing and Publishing | ||||||
USA: Chemicals and Chemical Products | ||||||
USA: Rubber and Plastics | ||||||
USA: Wholesale Trade and Commission Trade, | ||||||
Except of Motor Vehicles and Motorcycles | ||||||
USA: Retail Trade, Except of Motor Vehicles and | ||||||
Motorcycles; Repair of Household Goods | ||||||
USA: Hotels and Restaurants | ||||||
USA: Air Transport | ||||||
USA: Other Supporting and Auxiliary Transport | ||||||
Activities; Activities of Travel Agencies | ||||||
USA: Post and Telecommunications | ||||||
USA: Financial Intermediation | ||||||
USA: Renting of M&Eq and Other Business Activities | ||||||
USA: Other Community, Social and Personal Services | ||||||
ROW: Chemicals and Chemical Products | ||||||
4 | Rest of the world cluster | ROW: Mining and Quarrying | 3869 | Rest of the world cluster (C7) | ROW: Mining and Quarrying | 3264 |
ROW: Electricity, Gas and Water Supply | ROW: Electricity, Gas and Water Supply | |||||
ROW: Inland Transport | ROW: Inland Transport | |||||
ROW: Water Transport | ROW: Water Transport | |||||
ROW: Rubber and Plastics | ||||||
ROW: Renting of M&Eq and Other Business Activities | ||||||
5 | Canadian cluster | CAN: Mining and Quarrying | 1533 | Russian cluster | RUS: Mining and Quarrying | 1297 |
CAN: Pulp, Paper, Paper, Printing and Publishing | RUS: Basic Metals and Fabricated Metal | |||||
CAN: Coke, Refined Petroleum and Nuclear Fuel | RUS: Coke, Refined Petroleum and Nuclear Fuel | |||||
CAN: Electricity, Gas and Water Supply | RUS: Electricity, Gas and Water Supply | |||||
CAN: Wholesale Trade and Commission Trade, | RUS: Wholesale Trade and Commission Trade, | |||||
Except of Motor Vehicles and Motorcycles | Except of Motor Vehicles and Motorcycles | |||||
CAN: Chemicals and Chemical Products | RUS: Chemicals and Chemical Products | |||||
CAN: Inland Transport | RUS: Inland Transport | |||||
CAN: Agriculture, Hunting, Forestry and Fishing | ||||||
CAN: Wood and Products of Wood and Cork | ||||||
CAN: Basic Metals and Fabricated Metal | ||||||
CAN: Retail Trade, Except of Motor Vehicles and | ||||||
Motorcycles; Repair of Household Goods | ||||||
CAN: Renting of M&Eq and Other Business Activities | ||||||
CAN: Other Community, Social and Personal Services |