越览（141）——精读博士论文的3.3供应链网络结构性评价指标

摘要：This issue of tweets will introduce 3.3 Analysis of supply chain network structure indicators of the doctoral thesis "Research on

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“越览（141）——精读博士论文

《供应链网络结构视角下的产业链韧性研究》

的3.3供应链网络结构指标分析

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3.3 Analysis of supply chain network structure indicators

of "Yuelan (141) —— Intensive reading of

the doctoral dissertation

‘Research on the resilience of

the supply chain from the perspective of

supply chain network structure’".

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一、内容摘要（Summary of content）

本期推文将从思维导图、精读内容、知识补充三个方面介绍博士论文《供应链网络结构视角下的产业链韧性研究》的3.3供应链网络结构指标分析。

This issue of tweets will introduce 3.3 Analysis of supply chain network structure indicators of the doctoral thesis "Research on Industrial Chain Resilience from the Perspective of Supply Chain Network Structure" from three aspects: mind mapping, intensive reading content, and knowledge supplement.

二、思维导图（Mind mapping）

三、精读内容（Intensive reading content）

本节基于之前学者的研究，开展指标分析工作，包括节点指标分析与网络整体指标分析。节点指标方面，选取了点度中心性、介数中心性、离心度、接近中心性、特征向量中心性和聚类系数六个指标；网络整体指标方面，选取了密度、平均距离和网络直径三项指标。进一步地，本文采用熵权法结合TOPSIS方法，基于六个节点指标对企业的重要性进行综合评价，如下图所示。

Based on the research of previous scholars, this section conducts indicator analysis, including node indicator analysis and network overall indicator analysis. In terms of node indicators, six indicators are selected: point degree centrality, betweenness centrality, eccentricity, closeness centrality, eigenvector centrality and clustering coefficient; in terms of overall network indicators, three indicators are selected: density, average distance and network diameter. Furthermore, this paper adopts the entropy weight method combined with the TOPSIS method to comprehensively evaluate the importance of enterprises based on six node indicators, as shown in the figure below.

（一）网络节点指标（Network node metrics）

1.点度中心性（Degree centrality）

点度中心性用于衡量一个节点在网络中的直接连接数量。在有向供应链网络中，分为入度和出度两种类型。出度代表一个企业拥有的客户数量，出度越高，表明企业的合作范围越广；入度表示企业的供应商数量，入度越高，说明企业的供应来源更丰富。点度中心性为入度与出度之和，值越大说明该企业能接触到更多资源与信息，但并不代表其在网络中地位更高。

Degree centrality is used to measure the number of direct connections of a node in the network. In a directed supply chain network, it is divided into two types: in-degree and out-degree. Out-degree represents the number of customers an enterprise has. The higher the out-degree, the wider the scope of cooperation of the enterprise; in-degree represents the number of suppliers of the enterprise. The higher the in-degree, the richer the supply sources of the enterprise. Degree centrality is the sum of in-degree and out-degree. The larger the value, the more resources and information the enterprise can access, but it does not mean that it has a higher status in the network.

2.介数中心性（Betweenness centrality）

介数中心性反映了一个节点在网络中作为其他节点之间桥梁的程度，即该节点出现在网络中所有最短路径上的频率。在供应链网络中，介数中心性高的企业在信息传递和资源调配中处于关键位置，具备较强的控制能力和协调作用。通过归一化处理，可使不同规模网络下的介数中心性具备可比性。

Betweenness centrality reflects the degree to which a node acts as a bridge between other nodes in the network, that is, the frequency with which the node appears on all shortest paths in the network. In the supply chain network, enterprises with high betweenness centrality are in a key position in information transmission and resource allocation, and have strong control and coordination capabilities. Through normalization, the betweenness centrality of networks of different sizes can be made comparable.

3.离心度（Centrifugal）

离心度描述一个节点与网络中最远节点之间的距离。该值越大，表示该节点到其他节点的最长路径越长。在供应链网络中，离心度较大的企业，其下游或上游路径更长，可能意味着其影响范围更广或位于网络的边缘位置。

The eccentricity describes the distance between a node and the farthest node in the network. The larger the value, the longer the longest path from the node to other nodes. In the supply chain network, enterprises with larger eccentricity have longer downstream or upstream paths, which may mean that they have a wider range of influence or are located at the edge of the network.

4.接近中心性（Closeness centrality）

接近中心性衡量一个节点与网络中其他节点之间的接近程度。值越高，说明该节点平均距离其他节点更近，能够更快速地获取资源与信息，具有较强的沟通与协调潜力。在供应链网络中，接近中心性较高的企业更容易与其他企业建立业务联系，更具核心地位的潜力。

Closeness centrality measures the degree of proximity between a node and other nodes in the network. The higher the value, the closer the node is to other nodes on average, and the faster it can obtain resources and information, and the stronger its communication and coordination potential. In the supply chain network, companies with higher closeness centrality are more likely to establish business connections with other companies and have greater potential for core status.

5.特征向量中心性（Eigenvector centrality）

特征向量中心性综合考虑节点的连接数量及其连接对象的重要性。即一个节点不仅连接多，还需连接重要的节点，才能具备较高的特征向量中心性。在供应链网络中，拥有高特征向量中心性的企业可能处于资源流转和决策控制的核心位置，即使其连接数量不多，也可能通过关键合作关系获得较高影响力。

Eigenvector centrality comprehensively considers the number of connections of a node and the importance of its connected objects. That is, a node must not only have many connections, but also important nodes to have a high eigenvector centrality. In a supply chain network, companies with high eigenvector centrality may be at the core of resource flow and decision control. Even if they have few connections, they may gain high influence through key partnerships.

6.聚类系数（Clustering coefficient）

聚类系数反映某一节点的邻接节点之间的紧密程度。在供应链网络中，聚类系数越高，表示该企业的供应商和客户之间也存在合作关系，企业周围的网络结构较为密集；聚类系数较低说明企业所处网络较为松散，合作伙伴之间关联度不高。

The clustering coefficient reflects the closeness between the adjacent nodes of a node. In the supply chain network, the higher the clustering coefficient, the more cooperative relationships exist between the suppliers and customers of the enterprise, and the denser the network structure around the enterprise; the lower the clustering coefficient, the looser the network in which the enterprise is located, and the lower the degree of correlation between partners.

（二）网络整体指标（Overall network indicators）

1. 网络密度（Network density）

网络密度作为社会网络分析中的一个关键整体指标，用于衡量供应链网络中企业之间联系的紧密程度。密度值越接近于0，表示企业之间的关系越稀疏，合作与信息交流较少；密度值越接近于1，说明企业之间联系紧密、互动频繁。该指标有助于反映整个供应链网络的协同水平。

As a key overall indicator in social network analysis, network density is used to measure the closeness of connections between enterprises in the supply chain network. The closer the density value is to 0, the sparser the relationship between enterprises, and the less cooperation and information exchange; the closer the density value is to 1, the closer the connection between enterprises is and the more frequent the interaction. This indicator helps reflect the level of coordination of the entire supply chain network.

2. 平均距离（Average distance）

平均距离指的是网络中所有节点之间最短路径的平均值，用以衡量企业之间信息传播或业务合作的效率。路径越短，说明信息流通越快速、合作效率越高；路径越长，则表明网络中存在较多层级，企业间的互动和响应较慢。

The average distance refers to the average value of the shortest paths between all nodes in the network, which is used to measure the efficiency of information dissemination or business cooperation between enterprises. The shorter the path, the faster the information flow and the higher the cooperation efficiency; the longer the path, the more levels there are in the network, and the slower the interaction and response between enterprises.

3. 网络直径（Network diameter）

网络直径表示网络中最远的两个节点之间的最短路径长度，体现的是供应链的整体跨度和复杂程度。直径越大，表明供应链跨度越长，涉及企业越多；直径越小，则说明供应链结构更为紧凑，关联企业较少。

The network diameter indicates the shortest path length between the two farthest nodes in the network, reflecting the overall span and complexity of the supply chain. The larger the diameter, the longer the supply chain span and the more companies involved; the smaller the diameter, the more compact the supply chain structure and the fewer related companies.

（三）重要企业识别模型（Key enterprise identification model）

通过网络节点指标的分析，本文基于点度中心性、介数中心性、离心度、接近中心性、特征向量中心性和聚类系数六项指标，构建多属性决策模型，对供应链网络中企业的重要性进行综合评估。研究采用熵权法确定各指标权重，并结合TOPSIS方法对企业进行排序，从而识别在供应链网络中具有关键作用的企业，为构建更具韧性的供应链提供理论支持与改进方向。具体计算过程如下图所示：

Through the analysis of network node indicators, this paper constructs a multi-attribute decision-making model based on six indicators: degree centrality, betweenness centrality, eccentricity, closeness centrality, eigenvector centrality and clustering coefficient, to comprehensively evaluate the importance of enterprises in the supply chain network. The study uses the entropy weight method to determine the weight of each indicator, and combines the TOPSIS method to rank the enterprises, so as to identify enterprises that play a key role in the supply chain network, and provide theoretical support and improvement direction for building a more resilient supply chain. The specific calculation process is shown in the figure below:

1. 权重的确定（Determination of weights）

为科学确定各节点指标的权重，常用的方法包括层次分析法（AHP）、完全一致性方法（FUCOM）、基于水平的权重评估（LBWA）、CRITICAL法和熵权法。其中，AHP、FUCOM和LBWA属于主观赋权方法，受专家判断影响较大；CRITICAL虽为客观方法，但存在对归一化和数据聚合过程敏感的问题。相比之下，熵权法作为一种客观赋权方法，能够减少主观误差，充分利用原始数据信息，捕捉各指标间的潜在关联，因而本文采用熵权法进行指标权重计算。熵权法首先对各项节点指标进行标准化处理，然后通过计算每个指标的信息熵，最终确定各指标的客观权重。

In order to scientifically determine the weight of each node indicator, commonly used methods include the analytic hierarchy process (AHP), the full consistency method (FUCOM), the level-based weight assessment (LBWA), the CRITICAL method and the entropy weight method. Among them, AHP, FUCOM and LBWA are subjective weighting methods, which are greatly affected by expert judgment; although CRITICAL is an objective method, it is sensitive to normalization and data aggregation processes. In contrast, the entropy weight method, as an objective weighting method, can reduce subjective errors, make full use of original data information, and capture the potential correlation between indicators. Therefore, this paper adopts the entropy weight method to calculate the indicator weight. The entropy weight method first standardizes each node indicator, and then calculates the information entropy of each indicator to finally determine the objective weight of each indicator.

2.网络中重要企业识别（Identification of important companies in the network）

当前学者在综合性评估中采用了多种多属性决策方法，如决策试验与评价实验室（DEMATEL）、多属性边界近似区域比较法（MABAC）等。与这些方法相比，TOPSIS法（逼近理想解排序法）在指标排序方面表现更优，具有计算过程清晰、易于理解和广泛应用的优势。TOPSIS能够通过简单数学运算衡量各评价对象的相对优劣性。

At present, scholars have adopted a variety of multi-attribute decision-making methods in comprehensive evaluation, such as the Decision Experiment and Evaluation Laboratory (DEMATEL), the Multi-Attribute Boundary Approximation Area Comparison Method (MABAC), etc. Compared with these methods, the TOPSIS method (topic ideal solution ranking method) performs better in index ranking, with the advantages of clear calculation process, easy to understand and wide application. TOPSIS can measure the relative advantages and disadvantages of each evaluation object through simple mathematical operations.

为了提高评价精度，常将熵权法与TOPSIS法结合使用。熵权法能通过指标值的离散程度为各指标赋权，有效增强TOPSIS对不同指标信息的敏感度。

In order to improve the evaluation accuracy, the entropy weight method is often used in combination with the TOPSIS method. The entropy weight method can weight each indicator according to the discrete degree of the indicator value, effectively enhancing the sensitivity of TOPSIS to different indicator information.

TOPSIS法的基本思路是：首先构建加权归一化决策矩阵，然后确定正理想解（最优目标）与负理想解（最劣目标），接着分别计算各对象到这两种理想解的距离，最后通过距离比值计算综合评价值。综合评价值越大，说明企业在供应链网络中所处的位置越关键、作用越重要。

The basic idea of TOPSIS method is: first construct a weighted normalized decision matrix, then determine the positive ideal solution (optimal target) and the negative ideal solution (worst target), then calculate the distance of each object to these two ideal solutions, and finally calculate the comprehensive evaluation value through the distance ratio. The larger the comprehensive evaluation value, the more critical the position of the enterprise in the supply chain network and the more important its role.

The specific steps are as follows:

四、知识补充（Knowledge supplement）

决策试验与评价实验室法（DEMATEL，Decision-Making Trial and Evaluation Laboratory）是一种多属性决策分析方法，主要用于分析复杂系统中各因素之间的因果关系和影响程度。它最初由日立公司科学家提出，广泛应用于系统分析、管理决策、风险评估等领域。

The Decision-Making Trial and Evaluation Laboratory (DEMATEL) is a multi-attribute decision analysis method that is mainly used to analyze the causal relationship and influence degree between various factors in a complex system. It was originally proposed by scientists at Hitachi and is widely used in system analysis, management decision-making, risk assessment and other fields.

一个系统往往包含多个因素，这些因素之间不是独立存在的，而是相互影响的。例如，在一个企业韧性分析系统中，“供应多元化”、“信息透明度”、“应急响应能力”、“库存水平”之间可能存在复杂的正向或负向影响。

A system often contains multiple factors, which do not exist independently but influence each other. For example, in an enterprise resilience analysis system, there may be complex positive or negative effects between "supply diversification", "information transparency", "emergency response capability" and "inventory level".

传统方法往往无法处理这种复杂的双向依赖关系，而 DEMATEL 则通过构建因果影响矩阵和全路径传播模型，量化这种网络关系。

Traditional methods are often unable to handle such complex bidirectional dependencies, while DEMATEL quantifies such network relationships by constructing a causal influence matrix and a full-path propagation model.

The basic steps are as follows: