Analysis of ERGM Evolutionary Dynamics from a Multi-layer

Network Perspective: Based on New Energy Vehicle Industry Data

Hansong Zou

and Qin Liu

Wuhan University of Technology, Wuhan University of Technology, Wuhan, China

School of Management, Wuhan University of Technology, Wuhan, China

Keywords: Multi-layer Network, ERGM, Evolutionary Dynamics, Data Mining, Statistical Analysis.

Abstract: In the context of environment and energy bundle, the development of the economy has gradually entered into

a new state, and more and more countries have started to pay attention to the environment and ecological

development issues, and have made strategic deployment at the national macro level. In order to optimize the

green innovation network and promote the development of green innovation, this study, from the perspective

of a multi-layer network, uses the data of new energy vehicle patent citation, paper co-publication data, and

production supply relationship data from 2009 to 2020, constructs a multi-layer network including paper

knowledge network, innovation R&D network and production supply network to explore the evolution of

structural characteristics of new energy vehicle innovation network, and uses principal component analysis to

obtain knowledge capability and production capacity variables, and constructs ERGM model to analyze the

evolutionary dynamics of the multilayer network. The results show that the innovation level of the new energy

vehicle industry is closely related to the network structure; at the level of evolutionary dynamics, the number

of partners, the degree of similarity in production level is positively related to partnership formation, the

number of shared partners is negatively related to partnership formation, and the difference in knowledge

level has no significant determining effect on relationship formation.

1 INTRODUCTION

Under the background of resource environment and

energy constraint, more and more countries are

implementing the guiding measures of "innovation-

driven, quality-first, green development and

structural optimization". As a perfect combination of

green, innovation, and economic development, the

new energy vehicle industry, which belongs to the

manufacturing industry, has become an important

object of research for scholars. However, the current

new energy vehicle industry faces problems such as

imperfect innovation deployment, unbalanced

industrial layout, and insufficient innovation

efficiency. Therefore, it is important to explore the

evolution and layout of collaborative innovation and

industrial chain network of new energy vehicles and

identify the key factors affecting innovation

performance.

https://orcid.org/0000-0003

3094-7513

https://orcid.org/0000-0003-0719-148X

For the evolution of green innovation networks,

studies mainly focus on two perspectives: the

evolution of network structure and the dynamics of

network evolution. From the perspective of network

structure characteristics, at the level of evaluation of

influencing factors, Xu used the method of cluster

analysis to divide the development stages of new

energy vehicle technology innovation and

dynamically analyzed its network evolution in three

aspects: the overall network characteristics, the

location characteristics of innovation subjects, and

the distribution of the depth and breadth of

cooperation of innovation subjects (Xu 2020). In the

spatial and temporal dimensions, Cao et al. used the

social networks to analyze the network structure and

the evolution pattern of spatial distribution of the new

energy vehicle patent cooperation network during

1989-2015 (Cao 2019). Lee analyzed the evolution of

the network structure of collaborative inventions in

390

Zou, H. and Liu, Q.

Analysis of ERGM Evolutionary Dynamics from a Multi-layer Network Perspective: Based on New Energy Vehicle Industry Data.

DOI: 10.5220/0011346100003437

In Proceedings of the 1st International Conference on Public Management and Big Data Analysis (PMBDA 2021), pages 390-397

ISBN: 978-989-758-589-0

urban areas in the United States during 1979-2009

and found that the complexity of intercity networks

expanded and deepened, and technical collaborative

inventions were closely linked to core urban areas

(Lee 2016).

In the perspective of the evolutionary dynamic,

Ruan clarified the dynamics of technological

innovation network evolution and used ERGM to

analyze the evolutionary dynamics of OLED

technology innovation networks from five different

proximities: geographic, social, technological,

organizational, and institutional (Ruan 2018).

CSternitzke et al. found that collaborative

relationships among inventors can facilitate

knowledge interaction processes among inventor

collaborative network organizations (Csternitzke

2016).

Comprehensive domestic and international

literature reveals that existing system theories have

studied the structure, innovation dynamics,

innovation process, and innovation performance of

green innovation systems in traditional

manufacturing industries in a relatively detailed

manner, but the current research on innovation

networks often focuses only on a certain level of

R&D or industry, lacking the overall exploration of

the integration of innovation and industry chains. In

addition, in terms of perspective, it is more from the

perspective of a single-layer network and lacks the

analysis of the inter-layer linkage between innovation

and industrial multi-layer networks to achieve multi-

layer interaction among academia, innovation, and

industry.

Based on this, this study constructs a multilayer

network from the perspective of multilayer networks,

using the data of new energy vehicle thesis, patent

data, and supply relationship data to build a

multilayer network for the fusion of the three layers

of networks in the manufacturing industry, analyze

the structure and evolution trend of the multilayer

network, and use ERGM to explore the influence of

knowledge and production capacity on the evolution

of the innovation network. In order to analyze the

innovation ecological network of new energy

vehicles with the help of the multilayer network

theory, and to provide references for the construction

and optimization of the green innovation ecological

network of the national manufacturing industry.

2 DATA SOURCES AND

RESEARCH METHODS

2.1 Data Source and Processing

New energy vehicles, as the leading industry of green

innovation, exploring the technological innovation

network of it is representative and relevant. And

among many innovation achievements, patents are

the most widely used data in the field of innovation,

which are advanced and innovative (Zhao 2009), so

this paper selects the field of new energy vehicles as

the empirical object and uses patent R&D as a

measure of innovation performance.

In terms of data selection, this study selected 60

new energy vehicle innovation subjects including

BYD, Xiaopeng Automobile, Chery Automobile, and

other vehicle enterprises as research objects. Because

new energy vehicles formally entered the preparation

stage of R&D industrialization around 2008, before

that it was mostly the strategic layout stage with fewer

invention patents, and the patent data in 2021 is

incomplete, so the data period chosen in this paper is

2009-2020, and a three-tier network of academia,

research, and industry is established to analyze the

evolutionary characteristics and formation

mechanism of the innovation network of new energy

vehicles.

2.1.1 Knowledge Learning Layer

The knowledge layer network was based on the

publication of papers, and the paper data were

exported on CNKI, Google Scholar based on the

advanced search mode of vehicle enterprise + time.

Duplicates were excluded and 15033 papers were

obtained. With the vehicle enterprise as the node and

the university institution as the intermediary, a

cooperative relationship was established based on the

joint publication of author units, and 3963

connections were obtained by screening out non-

intermediated institutions and isolated nodes.

2.1.2 Patent R&D Layer

The R&D layer is based on patent data, and on the

website of incopat (https://www.incopat.com/), input

(AP=(vehicle enterprise)) AND (AD=[20090101 TO

20211004]), export data according to the vehicle

enterprise as a unit, and after screening out invalid

data, get 86,839 patents, and use patent citation After

filtering out the invalid data, we got 86,839 patents,

and using the citation and cited relationship to

Analysis of ERGM Evolutionary Dynamics from a Multi-layer Network Perspective: Based on New Energy Vehicle Industry Data

391

establish a connection, we got 19,063 times of patent

citation frequency.

2.1.3 Supply Production Layer

The supply chain layer is based on the supply

relationship of new energy vehicle battery, drive

motor, battery control, and motor control, and the data

is exported from the "MARK LINES Global

Automotive Information Platform" website

(https://www.marklines.com/cn/cn) according to the

classification of each segment to obtain a total of We

filtered out 1,435 data of vehicle enterprises in the

scope of our study, and established connections by

supplying parts to vehicle enterprises with the vehicle

as a unit, and obtained supply relationships 740 times.

2.2 Research Methods and Models

Based on the network data, we use python to read the

data to establish a three-layer network of learning,

research, and production, and analyze the laws and

trends of network evolution over time from the

perspective of the multi-layer network, and select two

extrinsic variables, knowledge learning, and supply

production, as well as patent R&D itself as an

intrinsic variable, to investigate the impact of multi-

layer network structure on enterprise innovation

performance. The multi-layer network structure is

shown in Figure 1.

Figure 1: Schematic diagram of the network structure.

2.2.1 Structural Feature Analysis

The evolutionary characteristics of the innovation

network are described at two levels: overall network

and individual. Since cooperation and innovation

performance has a lag effect (Liu 2021), based on a

lag period of three years, the data from 2009-2020 are

divided into 2009-2011, 2010-2012, 2011-2013,

2012-2014, 2013-2015, 2014-2016, 2015-2017,

2016- 2018, 2017-2019 nine stages to analyze the

evolutionary characteristics of the innovation

network structure.

2.2.2 Evolutionary Dynamics Analysis

In order to study the impact of multi-chain integration

on innovation networks, this paper uses principal

component analysis to measure the knowledge and

production levels of nodes with the help of

knowledge layer and industry layer indicators as

exogenous variables, and the degree, degree-sharing,

and edge-sharing of nodes in the innovation network

as endogenous variables to establish hypotheses to

build a model. Finally, the ERGM model is fitted to

diagnose the impact of the variables on the evolution

of the innovation layer network.

The general form of the ERGM is as follows:

𝑃(𝑌 = 𝑦) =

(())

()

(1)

where k is a constant ensuring that the probability of

a new network structure ranges from 0 to 1 and θ' is a

coefficient of the network structure statistic g(y).

Based on the above assumptions, an analytical

framework containing endogenous structural

variables and exogenous node attributes is

constructed, and the model architecture is

schematically shown in Figure 2:

3 ANALYSIS OF THE

EVOLUTION OF MULTI-

LAYER INNOVATION

NETWORKS

Using the Gephi import network matrix, the stage

network indicators and the Pearson correlation

coefficients between each indicator and innovation

performance were obtained as shown in Figure 2, and

the influence of network structure on innovation

performance was analyzed by observing the changes

of each network indicator selected to integrate

innovation performance.

1) The number of nodes, which indicates the

number of subjects involved in knowledge citation in

the patent citation network, can be used to measure

the scale of the knowledge innovation network of new

energy vehicles. The nodes of vehicle enterprises in

each time window from 2009 to 2020 grew from 15

to 58, and the scale of the network continuously

expanded and stabilized. The larger the network and

the richer the network resources, the more it

facilitates knowledge integration and exchange and

innovation (Jin 2020), which has a positive effect on

innovation performance positively.

vehicle enterprises

Universities and Institutions

Knowledge

learning layer

Innovative R&D

layer

Supply

roduction layer

promote

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2) The weighted average degree indicates the

average number of citations of patents in the current

window of each subject in the patent citation network,

which can be used to measure the closeness and

frequency of node connections in the knowledge

innovation network. As can be seen from the table,

the average degree shows a rising trend year by year

and the growth rate is steadily climbing, indicating

that the knowledge exchange among enterprises is

gradually frequent and close, which plays a role in

promoting knowledge innovation.

3) The agglomeration coefficient reflects the

formation and aggregation of community groups in

the network. It is also obvious from the table that with

the change of time, the clustering coefficient of the

patent citation network increases continuously and

stabilizes at about 0.8. It indicates that with the

passage of time, the knowledge cooperation among

enterprises in the new energy vehicle industry tends

to be more and more clustered and stable, forming a

joint development pattern centered on a small number

of strong enterprises.

Figure 2: Innovation Network Indicators.

4 STUDY OF THE

EVOLUTIONARY DYNAMICS

OF INNOVATION NETWORKS

4.1 Hypothesis Building

4.1.1 Endogenous Structural Variables

Network connections for technological innovation

have a certain preference, objects with high degree

nodes can be considered to have gained the

recognition of more companies and are more likely to

establish connections with other nodes in the choice

of companies, presenting as the basic side structure in

the network. However, network relationships are

established in long-term interactions between

subjects, after a long period of examination, learning,

and selection, and there are costs to be paid for

accumulating and maintaining network relationships,

requiring long-term and continuous investment in

relationship building, and when existing partners can

meet their own innovation needs, subjects are

reluctant to spend high costs to establish new

partnerships.

Therefore, the hypothesis is established that:

H1a: During the evolution of innovation

networks, nodes with a high degree tend to establish

new collaborations.

H1b: During the evolution of innovation

networks, nodes with a high degree tend to avoid

establishing new collaborations.

In the context of business innovation, sociologists

have coined the term 'transmissibility' to describe the

triadic sharing partnerships that are established

between firms. If both firm A and firm B are linked to

C, then firm C acts as a kind of intermediary, a

witness, and it is easier to build trust between A and

B, forming links that are presented as side and degree

sharing in the network.

Therefore, the hypothesis is established that:

H2a: Nodes with shared edges are more inclined

to establish new collaborations during the evolution

of innovation networks.

H3a: Degree sharing nodes are more inclined to

establish new collaborations during the evolution of

innovation networks.

4.1.2 Exogenous Attribute Variables

In addition to the characteristics of the location

structure of the nodes that affect the establishment of

network relationships, there are also attributes that are

inherent to the enterprises themselves that are

detached from the network structure. In order to study

the impact of chain integration of industry-academia-

research on enterprise innovation, this paper selects

two variables, knowledge level, and production level,

to explore their evolutionary dynamics.

In terms of knowledge level, the more similar the

knowledge level is, the more knowledge crossover

there is in the exchange process, the less costly it is to

transfer information and therefore the easier it is to

establish connections and the more efficient the

exchange of innovation is, which is explained by the

term 'homogeneity' in social networks. At the same

time, however, from another point of view, the

purpose of knowledge exchange is to complement

each other's strengths, and the closer the knowledge

of two companies is, the less benefit they can gain

from working with each other, and therefore the

similarity of knowledge levels may have the opposite

effect on the establishment of a partnership.

Analysis of ERGM Evolutionary Dynamics from a Multi-layer Network Perspective: Based on New Energy Vehicle Industry Data

393

Thus the hypothesis is established that:

H3a: During the evolution of an innovation

network, individuals with widely varying levels of

knowledge are more likely to form collaborative

relationships.

H3b: During the evolution of innovation

networks, individuals with similar levels of

knowledge are more likely to form collaborative

relationships.

In terms of production levels, as a business

enterprise, profit always comes first and a company's

production capacity determines to a certain extent the

ability to translate knowledge into real value, the

better the production capacity and production

conditions, the easier it is to attract companies to

establish connections.

Thus establishing the hypothesis that:

H4a: During the evolution of innovation

networks, cooperation is more likely to be established

between individuals with large differences in

production capacity.

H4b: During the evolution of innovation

networks, individuals with similar levels of

production are more likely to establish collaborative

relationships.

4.1.3 Calculation of Indicators of

Production Capacity and Knowledge

Level

There are two main types of indicators for an

enterprise's knowledge and production capacity.

The first category is its own attributes, for

example, the number of published papers can

represent its knowledge reserve, and the annual

output of an enterprise can measure its production

capacity. The second category is resource attributes,

which can be measured by their position in the

network.

In order to make a comprehensive measurement

of the knowledge level and production level of an

enterprise, this paper adopts the principal component

analysis method and uses SPSS to do principal

component analysis on the above variables, so as to

obtain a comprehensive score of knowledge level.

4.2 Study of the Evolutionary

Dynamics of ERGM Networks

4.2.1 Model Building

Based on the above hypothesis building, an analytical

framework containing endogenous structural

variables and exogenous node attributes is

constructed and the ERGM model is established as

follows.

𝑃

(

𝑋=𝑥

)





𝑒𝑥𝑝𝜃



Edges + 𝜃



Gwdsp +

𝜃



Gwesp + 𝜃



𝑛𝑜𝑑𝑚𝑎𝑡𝑐ℎ

(

Knowledge

)

𝜃



𝑛𝑜𝑑𝑒𝑐𝑜𝑣

(

Output

)

 (2)

The specific variables and associated explanations

are shown in Figure 3 below:

Figure 3: Explanation of indicators.

4.2.2 ERGM Analysis Results

The ERGM model was calculated using the Statenet

program package in the R environment, and the

model parameters were estimated using Markovian

Monte Carlo maximum likelihood estimation

(MCMC), and the model fit was assessed. The patent

citation cooperation network of new energy vehicle

enterprises from 2009 to 2020 was introduced as the

observation network. Model architecture as in Figure

Figure 4: Model architecture.

From the results, it can be seen in Figure 6 that

after adding the statistical terms in turn, Model4 has

the smallest AIC and BIC coefficients, indicating that

the model fits the observation network most closely.

From the specific fitting details, Figure 5 and

Figure 6 show the gap between each statistical term

of the model and the observation network. On the

whole, most of the indicators are concentrated near

the observation network, and as shown in Figure 7 the

deviation curve basically conforms to the normal

distribution characteristics and is concentrated near 0,

and each indicator fits better. From the degree

statistics results, the relationship between the number

of nodes of the simulated network and the

corresponding degree of the observed network can be

Model1

Model2

Model3

Goodness-of-fit test

Original model

Adding structural

dependencies

Adding knowledge

level

Adding production

capacity

MCMC Diagnosis

Model4

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seen in Figure 3, and it can be found that the number

of nodes of the observed network for each degree is

roughly contained between the maximum and

minimum values of the simulated network,

fluctuating in a small range above and below the

mean value. So it can be seen that the integrated

model of Model4 is closer to the observed network

than the more advanced model, and it is reasonable to

assume that the other model is more accurate than the

other models in terms of estimation results.

Figure 5: Comparison of indicators.

Figure 6: Degree Comparison.

Figure 7: Metrics statistics of the simulation model.

As shown in Figure 8. The endogenous structure

of the dependency estimation results show that degree

extension edges are positively correlated in

relationship formation, thus supporting hypothesis

H1a and rejecting hypothesis H1b. Degree-sharing

and edge-sharing are significantly negatively

correlated in relationship formation, rejecting H2a,

H2b, which may be explained by the fact that in the

process of network formation, in the early stage of

formation, in order to expand the scale and absorb

resources, shared partners may have a positive effect

on relationship formation. However, in the growth

stage and beyond, the innovation network has been

gradually improved, the functional overlap of the

subjects is very high, and the differences that exist are

relatively small, which means that the possibility of

Analysis of ERGM Evolutionary Dynamics from a Multi-layer Network Perspective: Based on New Energy Vehicle Industry Data

395

substitution is high. Firms choose to avoid sharing

their partners in order to safeguard their own interests

and to ensure the continued demand for themselves

by other subjects (Liu 2020).

The production capacity indicator Output is

significantly negatively correlated as a covariate and

positively correlated as a homogeneous indicator,

supporting hypothesis H4b and rejecting hypothesis

H4a, which implies that high production capacity is

not conducive to partnership building. The reason for

this may be that for large new energy vehicle

enterprises, which are prone to forming independent

production lines, they refuse to cooperate with small

new energy vehicle enterprises, choosing instead to

cooperate with similar enterprises on the basis of

other resource requirements for a win-win situation,

while for the few disadvantaged new energy

enterprises, they also lack the opportunity to

cooperate with large enterprises, thus reducing the

possibility of cooperation.

On the knowledge level indicator Knowledge, it is

significantly positively correlated as a covariate and

positively correlated as a homogeneous indicator, but

neither correlation is significant and thus for

hypothesis H3b, H3a cannot be judged. This suggests

that although firms with similar knowledge systems

are more likely to establish knowledge exchanges, the

crossover of knowledge systems in innovation R&D

is less likely to bring more benefits to both parties,

and the choice between benefits and exchange costs

depends on the needs of the firm.

Figure 8: Fitted coefficients for each model.

On the knowledge level indicator, it is

significantly negatively correlated when used as a

covariate and positively correlated when used as a

homogeneous type indicator, thus supporting

hypothesis H3b and rejecting hypothesis H3a, which

indicates that enterprises with similar knowledge

systems are more likely to establish knowledge

exchange, closer knowledge systems in innovation

R&D, and more likely to establish cooperation.

5 CONCLUSIONS

5.1 Main Research Conclusions

Based on the multilayer network perspective, this

study analyzes the trend of network structure

evolution and the evolutionary dynamics of the new

energy vehicle innovation network, and mainly draws

the following conclusions.

5.1.1 In the Process of Innovation Network

Evolution, the Number of Existing

Connection Relationships Is Positively

Correlated with Relationship

Formation

As can be seen in Figure 8, the coefficient on the

edges variable is positive, indicating that the number

of existing relationships is positively correlated with

relationship formation, suggesting a positive

feedback effect on the evolution of cooperative

relationships in network structures.

5.1.2 In the Evolution of Innovation

Networks, Shared Partners Are Not

Conducive to the Formation of New

Relationships

The analysis of the indicators in Figure 8 shows that

the coefficients of degree sharing (gwdsp) and side

sharing (gwesp) are negative and the correlation

between degree sharing and relationship formation is

high, indicating that sharing partners are not

conducive to relationship formation.

5.1.3 In the Process of Innovation Network

Evolution, the Degree of Similarity in

Production Level Is Positively Related

to Partnership, and the Level of

Knowledge Has No Significant Effect

on Relationship Formation.

As can be seen from Figure 8, production capacity

(Output) is negative when used as a covariate, while

it is positive when used as a covariate, indicating that,

the more individuals with similar production levels,

the more conducive to relationship formation. The

level of knowledge, however, is not significant as a

covariate or as a covariate and has no significant

effect on relationship formation.

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5.2 Recommendations

Multiple factors indicate that due to the gap in the

comprehensive capabilities of enterprises and the

control of resources caused by shared partners, strong

and weak enterprises are not conducive to

establishing connections, creating a bifurcation and

uneven distribution of resources in a certain

perspective, thus the state can introduce policies to

promote cooperation among multi-level enterprises

and give certain compensation to lead enterprises to

promote the balanced development of the industry.

5.3 Practical Implications and

Perspectives

This study from the perspective of multi-layer

networks, used the data of the new energy vehicle

industry to construct a three-layer network of

knowledge, innovation, and production. Through

principal component analysis to obtain variables, and

used the ERGM model to determine the influence of

variables on the formation of network relationships.

Due to the long time span of the data used in the

construction of the ERGM model, the different stages

of network formation are not fully used, and the

different evolutionary dynamics can be explored step

by step at a later stage by subdividing the network

formation stages.

ACKNOWLEDGEMENT

This work is supported by the Fundamental Research

Funds for the Central Universities (WUT:

2020VI028), and the National innovation and

entrepreneurship training program for college

students S202110497050 and S202110497061.

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