Manufacturing enterprise collaboration network: An empirical research and evolutionary model

Fig. 2. MECN visualization. Red nodes are OEMs and blue nodes are part suppliers.

Fig. 3. MLE fit of degree distribution of (a) OEMs and (b) part suppliers.

Fig. 4. Degree correlation in one-mode projection network on (a) OEMs and (b) part suppliers.

Fig. 5. MECN evolutionary model construction process.

Fig. 6. MECN evolutionary model visualization. Red nodes are OEMs and blue nodes are part suppliers.

Fig. 7. Distributions of the evolutionary model (blue), compared with empirical network (red) and the degree-based model (green), showing (a) the degree distribution of OEMs, and (b) degree distribution of part suppliers.

Table 1. Information about part suppliers (a portion).

Table 1. Information about part suppliers (a portion).

No	Part suppliers	Found year	Location	Registered capital	Number of intellectual properties	Number of risk warnings
1	Guangzhou Qicheng Auto Parts Co., Ltd.	2013	Guangdong	2.0 × 10⁶ CNY	1	6
2	Shenyang Pinghe Valeo Automotive Transmission System Co., Ltd.	2013	Liaoning	3.5 × 10⁷ USD	16	4
3	Shanxi Zhongjin Industrial Machinery Co., Ltd.	1996	Shanxi	8.0 × 10⁶ CNY	29	1
4	Conde Ryan electromagnetic technology (China) co., Ltd.	2005	Jiangsu	9.8 × 10⁶ EUR	23	0
5	Shanghai saks powertrain components system co., Ltd.	2001	Shanghai	1.4 × 10⁷ USD	89	4

Table 2. Topological properties of empirical MECN.

Table 2. Topological properties of empirical MECN.

Topological properties	Result
OEMs	245
Part suppliers	6790
Edges	20938
Part suppliers per OEM	85.46
OEMs per part suppliers	3.08
Average path length L	3.755
Clustering coefficient c	0.253
Assortativity coefficient r	−0.480
(one-mode projection on OEMs)	−0.231
Assortativity coefficient r_M	−0.231
(one-mode projection on part suppliers)	−0.021
Assortativity coefficient r_S	−0.021
OEM degree	Max: 963 and Min: 1
Part supplier degree	Max: 23 and Min: 1

Table 3. Degree distribution fitting results of empirical MECN.
View table
View in Article
Table 3. Degree distribution fitting results of empirical MECN.
Distribution p(k) D (OEM) D (part supplier)
Power law k^−α 0.2107 0.1309
Truncated power law k^−αe^−αk 0.0545 0.0372
Exponential e^−λk 0.3260 0.0301
Stretched exponential (λk)^{β – 1}e^{−(λk)^β} 0.0649 0.0203

Table 4. Notations used in evolutionary model.

Table 4. Notations used in evolutionary model.

Notation	Meaning
t	time step of evolution
u₀,v₀,e₀	initial number of OEM nodes, part supplier nodes, and edges respectively
e	number of edges
n_M,n_S,n_E	maximum number of OEM nodes, part supplier nodes, and edges respectively
k_i,k_j	degree of nodes i and j respectively
f_i,f_j	fitness of nodes i and j calculated by the entropy-TOPSIS method respectively
d_{max_s}, d_{max_m}	maximum number of part supplier nodes that OEM nodes can connect with
d_{max_s}, d_{max_m}	maximum number of OEM nodes that part supplier nodes can connect with
S_ij	probability of successful connection between nodes i and j
q	parameter that affects where the link is deleted (from local-world or global network)
Q_i	probability of being selected as local-world network for node i

Table 5. Results of topological properties.

Table 5. Results of topological properties.

Topological properties	Empirical network	Evolutionary model	Degree-based model
OEMs	245	245	245
Part suppliers	6790	6790	6790
Edges	20938	20938	20938
Part suppliers per OEM	85.46	85.46	85.46
OEMs per part supplier	3.08	3.08	3.08
Average path length L	3.755	3.760 ± 0.015	3.854 ± 0.015
Clustering coefficient c	0.253	0.224 ± 0.002	0.219 ± 0.02
Assortativity coefficient r	−0.480	−0.417 ± 0.030	−0.534 ± 0.040
Assortativity coefficient r_M	−0.231	−0.265 ± 0.020	−0.203 ± 0.020
(one-mode projection on OEMs)	−0.231	−0.265 ± 0.020	−0.203 ± 0.020
Assortativity coefficient r_S	−0.021	−0.044 ± 0.015	−0.034 ± 0.015
(one-mode projection on part suppliers)	−0.021	−0.044 ± 0.015	−0.034 ± 0.015
OEM degree	Max: 963 Min: 1	Max: 949 ± 1 Min: 1	Max: 600 ± 150 Min: 1
Part supplier degree	Max: 23 Min: 1	Max: 22 ± 2 Min: 1	Max: 21 ± 2 Min: 1

Table 6. RMSD results of topological properties.