## 3.1 Measurement results

In this paper, 11 indicators are selected to measure the comprehensive logistics level of each city. Take the city quality of Sichuan Province in 2016 as an example; SPSS software is used for principal component analysis(Table2)。

Table.2 Eigenvalue and variance contribution rate

Component | Initial Eigenvalues | Extraction Sums of Squared Loadings | Rotation Sums of Squared Loadings |

| Total | % of Variance | Cumulative % | Total | % of Variance | Cumulative % | Total | % of Variance | Cumulative % |

1 | 8.381 | 76.187 | 76.187 | 8.381 | 76.187 | 76.187 | 7.956 | 72.323 | 72.323 |

2 | 1.700 | 15.454 | 91.642 | 1.700 | 15.454 | 91.642 | 2.125 | 19.318 | 91.642 |

3 | 0.423 | 3.841 | 95.483 | | | | | | |

4 | 0.314 | 2.855 | 98.338 | | | | | | |

5 | 0.156 | 1.422 | 99.760 | | | | | | |

6 | 0.011 | 0.099 | 99.859 | | | | | | |

7 | 0.007 | 0.062 | 99.921 | | | | | | |

8 | 0.006 | 0.051 | 99.973 | | | | | | |

9 | 0.002 | 0.014 | 99.987 | | | | | | |

10 | 0.001 | 0.010 | 99.997 | | | | | | |

11 | 0.000 | 0.003 | 100.000 | | | | | | |

It can be found from Table 2 that the cumulative variance contribution rate of the first two principal components is 91.642%, and their eigenvalues are all greater than 1, indicating that they cover most of the critical information of 11 data.

Orthogonal rotation of the variance maximization of the factor load matrix is carried out (Table3). After rotation, the two principal components' factor coefficients begin to show polarization, which can better explain the index data's attributes. The first principal component coefficient is close to 1 with 9 indexes, and the coefficient of the second principal component is larger with 2 indexes. The index with a large first principal component coefficient mostly describes the development status of urban logistics, and the description of logistics activity potential is more material promotion. However, the index with a larger principal component coefficient is positioned as the driving force of urban development and the prospect, emphasizing the leverage effect of investment concentration in the whole society.

Table.3 The rotated factor load matrix

| Component 1 | Component 2 |

Freight Ton-kilometers of Highways | 0.816 | 0.240 |

Number of Employed Persons in Transport, Storage and Post | 0.971 | 0.188 |

Total Length of Highways | 0.093 | 0.957 |

Total Investment in Fixed Assets | 0.963 | 0.230 |

Public Budget Expenditure in Transport | 0.356 | 0.827 |

Gross Regional Product | 0.980 | 0.172 |

Per Capita Gross Regional Product | 0.746 | -0.425 |

Tertiary Industry | 0.974 | 0.206 |

Total Imports and Exports | 0.968 | 0.193 |

Total Retail Sales of Consumer Goods | 0.975 | 0.195 |

Number of Mobile Telephones Subscribers | 0.963 | 0.226 |

It can be seen from Table 4 that Chengdu's first principal component score is significantly higher than other cities, and the city quality measurement result is also the largest. This shows that Chengdu attaches more importance to logistics activities and has a good foundation for the logistics development. The second principal component score of Ganzi is the highest, indicating that Sichuan province has begun to gradually pay attention to the transportation inconvenience of the western Sichuan region, realized the importance of a good logistics network, and intended to make it a significant thrust for the optimization of the structure and function of logistics network in Sichuan Province。

In Table2, the variance contribution rate is taken as the weight, and the calculation formula of city quality is:

$$M=\frac{{V}_{1}}{{V}_{1}+{V}_{2}}FAC1+\frac{{V}_{2}}{{V}_{1}+{V}_{2}}FAC2$$

11

Since the negative number of urban mass is not convenient to continue to calculate the gravitational strength of each city's logistics, the results are parallel and amplified, and the newly adjusted urban mass\({\text{M}}^{\text{'}}=(M+6)\times 10\)

Table.4 Quality measurement results of cities in Sichuan Province in 2016

Cities | FAC1 | FAC2 | \(M\) | \({M}^{\text{'}’}\) |

Chengdu | 4.196 | 0.938 | 3.216 | 92.160 |

Zigong | 0.019 | -1.095 | -0.198 | 58.022 |

Panzhihua | 0.273 | -1.921 | -0.174 | 58.265 |

Luzhou | 0.009 | -0.072 | -0.007 | 59.925 |

Deyang | 0.152 | -1.071 | -0.097 | 59.029 |

Mianyang | -0.031 | 0.302 | 0.036 | 60.362 |

Guangyuan | -0.492 | 0.554 | -0.248 | 57.516 |

Suining | -0.253 | -0.642 | -0.307 | 56.929 |

Neijiang | -0.206 | -0.661 | -0.277 | 57.231 |

Leshan | 0.042 | -0.395 | -0.046 | 59.542 |

Nanchong | -0.253 | 0.932 | -0.003 | 59.973 |

Meishan | -0.124 | -0.818 | -0.248 | 57.521 |

Yibin | -0.153 | 0.238 | -0.065 | 59.355 |

Guangan | -0.234 | -0.616 | -0.289 | 57.113 |

Dazhou | -0.119 | 0.538 | 0.017 | 60.175 |

Yaan | -0.283 | -0.555 | -0.312 | 56.880 |

Bazhong | -0.583 | 0.477 | -0.330 | 56.705 |

Ziyang | -0.188 | -0.302 | -0.194 | 58.060 |

Aba | -0.504 | 0.180 | -0.330 | 56.704 |

Ganzi | -0.992 | 2.624 | -0.211 | 57.892 |

Liangshan | -0.276 | 1.367 | 0.064 | 60.641 |

## 3.2 Analysis of the Spatial Correlation Structure

## 3.2.1 The whole logistics

The modified gravity model was used to calculate the numerical value of the interaction in the logistics network formed between cities, and then binarization was carried out to construct the association structure matrix. Ucinet software is used to draw the network association structure diagram shown in Figure 2. In this paper, the year 2010 (correlation number is 105), 2013 (correlation number is 111), 2016 (correlation number is 116), and 2018 (correlation number is 114) are selected as representative data to be drawn. The four network correlation structure charts reflect the connectivity of logistics relations between cities. It can be seen from Figure 2 that from 2010 to 2018, the number of connections continued to increase, and the logistics activities between cities have become closer. Sichuan Province has realized the sharing of some resources and infrastructure and has increased its resistance to economic fluctuations, which has promoted the coordinated development of logistics networks to a certain extent.

In 2010, the number of spatial correlations was 105 and kept rising until 2013, when the number reached 111. In the following two years, the number was flat. However, in 2016, there was a relatively noticeable change, which was also the year with the most spatial correlation among the nine years of data studied in this paper, rising to 116. Since then, it has shown a smaller decline. After 115 in 2017, the number of correlations dropped to 114 in 2018. The above data shows that the spatial correlation structure of logistics in Sichuan Province is complex, and cities' connections are close. There is still much room for improvement in the coordination and cooperation capabilities between logistics nodes and the logistics network's stable operation.

As shown in Figure 3, Sichuan's logistics network's overall density rose from 0.250 in 2010 to 0.271 in 2018. In 2011 and 2016, the overall density showed a particular leapfrog development, growing by 3.8% and 5.5%, respectively, compared with the previous year. The improvement of correlation number and network density directly depicts the gradual improvement process of logistics network in Sichuan province, which is in an excellent running state and reflects specific spillover effect, which strongly promotes the mutual learning and integration of facilities, technologies, and policies among cities in the province. According to the calculation, the network correlation between 2010 and 2018 is all 1, indicating that the logistics network's daily operation in Sichuan province is smooth, with a low possibility of rupture and overall solid robustness.

## 3.2.2 Individual Logistics Network

To further study each region's position in Sichuan logistics' spatial association structure, this paper selects 2016 as the representative, and analyzes the degree centrality, betweenness centrality, and closeness centrality.

It can be seen from Table 5, the average degree of 21 cities in Sichuan province is 41.905, and 10 cities above this value. They are located in the central region of Sichuan province, which has a sure economic foundation and a bright prospect of logistics development. For the Outdegree, Suining, Bazhong, Ganzi, and Aba all reach 8, which is in a high-value position. The city with the smallest Outdegree is Mianyang, which is only 2. This difference is that Ganzi and Aba account for approximately 48.80% of the total area of Sichuan Province and are rich in mineral resources, animal and plant resources. It is necessary to export resources further to transform them into financial ability and economic advantage.

From the analysis of InDegree, the cities with an InDegree greater than 10 are Chengdu, Ziyang, Deyang, and Zigong. It can be seen from this that Chengdu and surrounding cities have high logistics attracting capacity, which is inseparable from the acceleration of infrastructure construction, investment promotion, and talent introduction in Sichuan Province in recent years. It has given the city of Chengdu too high economic vitality and has even begun to promote Sichuan province's development positively. With an InDegree of 0, Aba is in the least active position in the overall logistics network.

Cities with a high Outdegree are mainly concentrated in the eastern part of Sichuan province, directly bordering other fast-growing regions around or some cities scattered in all directions with Chengdu as the center. The Outdegree in Sichuan province is controlled at a relatively stable level, indicating that the overall logistics activities have strong synergies, which transcend geographical conditions and form a wide range of netlike logistics connections. Meanwhile, some developed cities promote the stability of related structures with their development gravity. Cities with high InDegree form an approximate circle, indicating that logistics activities are highly concentrated. Regional isolation has not yet been broken, and it is less attractive to peripheral cities' logistics.

Table.5 Degree centrality of logistics spatial network in Sichuan province in 2016

Cities | OutDegree | InDegree | Centrality | Rank |

Chengdu | 5 | 17 | 85.000 | 1 |

Zigong | 4 | 10 | 50.000 | 5 |

Panzhihua | 5 | 1 | 25.000 | 18 |

Luzhou | 5 | 2 | 25.000 | 18 |

Deyang | 3 | 11 | 55.000 | 3 |

Mianyang | 2 | 6 | 30.000 | 15 |

Guangyuan | 7 | 1 | 35.000 | 14 |

Suining | 8 | 6 | 55.000 | 3 |

Neijiang | 3 | 9 | 45.000 | 8 |

Leshan | 7 | 6 | 40.000 | 11 |

Nanchong | 3 | 5 | 30.000 | 15 |

Meishan | 7 | 7 | 50.000 | 5 |

Yibin | 5 | 4 | 25.000 | 18 |

Guangan | 6 | 5 | 45.000 | 8 |

Dazhou | 6 | 1 | 30.000 | 15 |

Yaan | 6 | 6 | 45.000 | 8 |

Bazhong | 8 | 2 | 40.000 | 11 |

Ziyang | 7 | 13 | 65.000 | 2 |

Aba | 8 | 0 | 40.000 | 11 |

Ganzi | 8 | 3 | 50.000 | 5 |

Liangshan | 3 | 1 | 15.000 | 21 |

Mean | 5.524 | 5.524 | 41.905 | |

It can be seen from Table 6, the top three cities with betweenness centrality are Ziyang, Chengdu, and Suining. Their betweenness centrality accounts for a total of 165.65, accounting for 56.73% of the total cities. The top-ranking cities are located in the central part of Sichuan Province, which are the main economic activity areas in the province and have sufficient logistics development conditions. The betweenness centrality of Nanchong, Guangyuan, Mianyang, Aba, Dazhou, and Liangshan are all 0, and these cities are located on the edge of Sichuan Province. It is challenging to produce the scale effect of industrial agglomeration, and the ability to promote the development of the overall logistics network is weak.

Table.6 Closeness Centrality of logistics spatial network in Sichuan province in 2016

Cities | InCloseness | QutCloseness | Centrality | Rank |

Chengdu | 86.957 | 13.072 | 86.957 | 1 |

Zigong | 62.500 | 12.821 | 64.516 | 7 |

Panzhihua | 5.000 | 16.949 | 55.556 | 19 |

Luzhou | 40.000 | 12.987 | 57.143 | 15 |

Deyang | 68.966 | 12.658 | 68.966 | 3 |

Mianyang | 54.054 | 12.121 | 57.143 | 15 |

Guangyuan | 5.249 | 21.053 | 58.824 | 14 |

Suining | 54.054 | 13.423 | 68.966 | 3 |

Neijiang | 60.606 | 12.739 | 62.500 | 10 |

Leshan | 58.824 | 13.423 | 62.500 | 10 |

Nanchong | 38.462 | 12.821 | 57.143 | 15 |

Meishan | 60.606 | 13.423 | 66.667 | 5 |

Yibin | 45.455 | 13.072 | 47.619 | 21 |

Guangan | 38.462 | 13.245 | 64.516 | 7 |

Dazhou | 5.249 | 20.833 | 57.143 | 15 |

Yaan | 44.444 | 13.245 | 64.516 | 7 |

Bazhong | 5.263 | 21.277 | 60.606 | 13 |

Ziyang | 74.074 | 13.514 | 74.074 | 2 |

Aba | 4.762 | 15.504 | 62.500 | 10 |

Ganzi | 32.258 | 13.514 | 66.667 | 5 |

Liangshan | 5.000 | 16.260 | 50.000 | 20 |

Mean | 40.488 | 14.664 | 62.596 | |

## 3.2.3 Network Block

In the block model analysis, the adjusted maximum segmentation depth is 2, and the convergence standard is 0.2. Therefore, according to the spatial clustering characteristics of the logistics network in Sichuan Province, 21 cities can be divided into four plates with different commonalities, as shown in Figure 4.

The correlation number of the overall logistics network in Sichuan province in 2016 is 116. Table 7 shows that the number of relationships within the four blocks is 65, and the number of connections between the four blocks is 51, indicating that the overall logistics development of Sichuan Province is based on urban agglomerations. The urban part of the first plate is located in the Chengdu Plain Economic Zone, and it also includes the entire area of the Northwest Sichuan Ecological Economic Zone and the Panxi Economic Zone and covers the western part of Sichuan Province. The second section covers some cities in the Southern Sichuan Economic Zone and the Chengdu Plain Economic Zone, and is located in the southeast of Sichuan Province. The third plate is located in the central part of Sichuan, close to Chengdu. The fourth sector belongs to cities in the Northeast Sichuan Economic Zone and is the center of regional economic integration between Sichuan, Chongqing, Shaanxi, and Gansu. The spatial relationship within the urban agglomeration is stable, and there are spillover effects that cannot be ignored in the logistics activities between the plates.

Table.7 Spillover effect of logistics network space-related plate in Sichuan province in 2016

Plate | Number of acceptance relations | Number of emitted relations | The ratio of expected internal relationships(%) | Actual internal relationship ratio(%) |

| In the plate | Outside the plate | In the plate | Outside the plate | | |

1st | 21 | 14 | 21 | 21 | 30.00 | 50.00 |

2ed | 23 | 21 | 23 | 8 | 25.00 | 74.19 |

3rd | 2 | 15 | 2 | 3 | 5.00 | 40.00 |

4th | 19 | 1 | 19 | 19 | 25.00 | 50.00 |

The total number of relations emitted by the first plate is 42, among which 21 are generated within the plate. The expected proportion of internal links is 30%, while the actual ratio of internal relations is 50%, called a two-way overflow plate. The number of relationships generated inside the second plate is 23, and there are 8 relationships outside the plate. The expected ratio of internal relationships is 25%, and the actual ratio of internal relationships is 74.19%, serving as the net benefit plate. The third plate gives out 5 correlation relations and produces 2 internally. The expected ratio of internal relations is 5%, but the actual ratio of internal relations is 40%, the main beneficiary plate. The number of relations emitted from the fourth plate's interior is 19, and the same number of relations are emitted from the exterior plate. The expected proportion of internal relations is 25%, while the actual ratio of internal relations is 50%, considered the economic man plate.

## 3.3 Analysis of the Influencing Factors

According to the calculation results of 5000 random substitutions, the results are shown in table 8. The development investment of the urban commercial business has a substantial impact on the professional development of the city's logistics. The reason for this result may be that the existing logistics activities are mostly based on commodity circulation. However, the correlation coefficient between the logistics specialization matrix \({L}_{i}\) and the betweenness centrality \(B\)is not significant, indicating that the logistics mode of the node city as a logistics intermediary is single. The degree centrality \(D\), the closeness centrality \(C\), the science and technology research grants \({S}_{a}\) and the number of trucks \(I\) are calculated to reflect their positive influence on the degree of professional development of urban logistics.

Table.8 The results of QAP correlation analysis

Variable | Actual correlation coefficient | Significance level | Mean correlation coefficient | Standard deviation | Min | Max | P≥0 | P≤0 |

\(D\) | 0.638 | 0.026 | 0.001 | 0.174 | -0.148 | 0.697 | 0.026 | 0.974 |

\(C\) | 0.676 | 0.044 | 0.002 | 0.190 | -0.150 | 0.726 | 0.044 | 0.956 |

\(B\) | 0.333 | 0.102 | 0.004 | 0.191 | -0.125 | 0.728 | 0.102 | 0.898 |

\({S}_{a}\) | 0.697 | 0.020 | 0.003 | 0.209 | -0.119 | 0.759 | 0.020 | 0.980 |

\(I\) | 0.953 | 0.025 | -0.001 | 0.215 | -0.100 | 0.967 | 0.025 | 0.975 |

\({C}_{i}\) | 0.985 | 0.005 | 0.004 | 0.229 | -0.082 | 0.988 | 0.005 | 0.995 |