Analysis on the evolution of the urban network of the urban agglomeration in the middle reaches of the Yangtze River and its influencing factors: From the perspective of multi factor flow

doi:10.3969/j.issn.1004-9479.2024.10.20222209

Abstract

Abstract:

Based on multivariate data such as the Baidu index, mileage data, and co-authored paper data, a multi-city network was constructed, then social network analysis was used to explore the evolution characteristics of multi-city network structure in the middle reaches of the Yangtze River from 2011 to 2019, and the QAP model was used to analyze its influencing factors. The results show that: (1) The density of multiple networks in the middle reaches of the Yangtze River from 2011 to 2019 is less than 0.5, but the relationship between cities has gradually becoming closer. In addition, the "small world" characteristisc of each network is obvious, and the hierarchical structure of urban nodes conforms to the rank-size distribution characteristics. (2) The diversity of multiple network structures is obvious, the core skeleton of the information network has not changed significantly, while the change of the economic network skeleton is obvious, the traffic network gradually presents an H-shaped structure, and the innovation network tends to be flat and complex. (3) The centrality of city nodes in the multi-city network has obvious differences. Wuhan, Changsha, and Nanchang are stable network hubs, and the urban agglomeration in the middle reaches of the Yangtze River forms four condensed subgroups, which are mainly related within subgroups. (4) There are strong similarities and differences among multiple networks. Spatial proximity, administrative relationship, level of economic development, and intensity of policy intervention have significant effects on the structure of multiple networks to different degrees.

Key words: multi-city network, social network analysis, QAP model, influencing factors, urban agglomeration in the middle reaches of the Yangtze River

摘要：

基于百度指数、里程数据及论文合著数据等多元数据，构建多重城市网络，采用社会网络分析法探究2011—2019年长江中游城市群多重城市网络结构的演变特征，并运用QAP模型分析其影响因素。研究发现：（1）2011—2019年长江中游城市群多重网络密度均小于0.5，但城市之间的联系逐渐密切，此外，各网络的“小世界”特征明显，城市节点的等级结构符合位序-规模分布特征；（2）多重网络结构存在显著差异，信息网络核心骨架未发生明显变化，经济网络骨架逐渐明显，交通网络逐渐呈现出“工”字形结构，创新网络趋向扁平化、复杂化；（3）多重城市网络城市节点的中心性具有较为明显的差异性特征，武汉、长沙、南昌的网络枢纽地位较为稳定；长江中游城市群形成4个凝聚子群，城市间联系以子群间关联为主；（4）多重网络之间具有较强的相似性及差异性，空间邻近、行政关系、经济发展水平及政策干预强度等因素对多重网络结构产生不同程度的显著影响。

关键词: 多重城市网络, 社会网络分析, QAP模型, 影响因素, 长江中游城市群, 多元要素流

He LIU, Xueming LI, Yilu GONG. Analysis on the evolution of the urban network of the urban agglomeration in the middle reaches of the Yangtze River and its influencing factors: From the perspective of multi factor flow[J]. World Regional Studies, 2024, 33(10): 100-115.

刘贺, 李雪铭, 宫一路. 长江中游城市群城市网络演化及影响因素[J]. 世界地理研究, 2024, 33(10): 100-115.

Figures/Tables 11

Tab.1 Complex characteristics analysis index of multiple urban networks

指标	计算公式	变量解释
网络密度	$D = L N (N - 1)$	D为城市网络密度，L为城市网络中实际存在的联系，N为城市网络中节点的数量
聚类系数	$C = 1 N ∑ N i ⊂ N C i$	C为城市网络的聚类系数，N为城市网络中节点的数量，C_i 为节点的聚类系数
平均路径长度	$L = 2 N (N - 1) ∑ i ≠ j d i j$	L为平均路径长度，N为城市网络中节点的数量，d_ij 为两城市节点之间的路径长度
度中心性	$C D i = ∑ j x i j / (N - 1)$	CD_i 为第i个城市的度中心性，N为城市网络中节点的数量，x_ij 为城市i与城市j之间的要素联系强度
中介中心性	$C B i = ∑ j = N ∑ k = N g j k (i) g j k (j ≠ k ≠ i)$	CB_i 为第i个城市的中介中心性，g_jk 为城市j与城市k之间的最短路径数量，g_jk(i)为节点i穿过城市j与城市k之间的最短路径的数量

Tab.1 Complex characteristics analysis index of multiple urban networks

指标	计算公式	变量解释
网络密度	$D = L N (N - 1)$	D为城市网络密度，L为城市网络中实际存在的联系，N为城市网络中节点的数量
聚类系数	$C = 1 N ∑ N i ⊂ N C i$	C为城市网络的聚类系数，N为城市网络中节点的数量，C_i 为节点的聚类系数
平均路径长度	$L = 2 N (N - 1) ∑ i ≠ j d i j$	L为平均路径长度，N为城市网络中节点的数量，d_ij 为两城市节点之间的路径长度
度中心性	$C D i = ∑ j x i j / (N - 1)$	CD_i 为第i个城市的度中心性，N为城市网络中节点的数量，x_ij 为城市i与城市j之间的要素联系强度
中介中心性	$C B i = ∑ j = N ∑ k = N g j k (i) g j k (j ≠ k ≠ i)$	CB_i 为第i个城市的中介中心性，g_jk 为城市j与城市k之间的最短路径数量，g_jk(i)为节点i穿过城市j与城市k之间的最短路径的数量

Tab. 2 Indicators of multiple urban network development in urban agglomerations in the middle reaches of the Yangtze River

网络	2011年			2019年
网络	网络密度	集聚系数	平均路径长度	网络密度	集聚系数	平均路径长度
信息网络	0.339	0.786	1.709	0.360	0.796	1.640
经济网络	0.230	0.802	1.828	0.397	0.842	1.603
交通网络	0.268	0.782	1.990	0.293	0.799	1.883
创新网络	0.095	0.694	2.307	0.130	0.798	2.201

Fig.1 Weighting degree order of urban agglomerations in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

Fig.2 Network hierarchy characteristics of urban agglomeration in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

Tab.3 Network degree centrality of urban agglomeration in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

城市	信息网络		经济网络		交通网络		创新网络
城市	2011年	2019年	2011年	2019年	2011年	2019年	2011年	2019年
南昌	44.444/2	59.259/3	55.556/3	66.667/3	14.879/3	19.596/3	44.444/2	48.148/2
景德镇	7.407/9	18.519/12	11.111/20	7.407/26	0.568/27	2.179/24	7.407/9	3.704/14
萍乡	3.704/15	14.815/15	22.222/8	7.407/26	8.840/8	12.104/6	3.704/15	3.704/14
九江	7.407/9	22.222/9	14.815/14	22.222/8	4.013/17	5.931/16	7.407/9	7.407/10
新余	3.704/15	11.111/19	25.926/6	3.704/28	8.337/9	9.961/10	3.704/15	3.704/14
鹰潭	3.704/15	7.407/24	3.704/28	11.111/21	10.040/6	12.092/7	3.704/15	0.000/28
吉安	7.407/9	11.111/19	22.222/8	14.815/12	2.658/23	2.735/23	7.407/9	3.704/14
宜春	3.704/15	25.926/6	18.519/10	14.815/12	7.291/11	9.949/11	3.704/15	3.704/14
抚州	3.704/15	11.111/19	11.111/20	11.111/21	3.342/19	4.369/20	3.704/15	11.111/6
上饶	3.704/15	25.926/6	18.519/10	14.815/12	8.220/10	11.874/8	3.704/15	3.704/14
武汉	70.370/1	92.593/1	96.296/1	100.000/1	21.771/1	24.861/2	70.370/1	66.667/1
黄石	3.704/15	11.111/19	18.519/10	14.815/12	3.239/20	5.217/17	3.704/15	3.704/14
宜昌	7.407/9	29.630/4	33.333/4	37.037/4	6.220/13	6.621/14	7.407/9	11.111/6
襄阳	3.704/15	29.630/4	18.519/10	33.333/5	3.394/18	3.256/22	3.704/15	7.407/10
鄂州	3.704/15	7.407/24	7.407/23	14.815/12	3.188/21	4.999/19	3.704/15	3.704/14
荆门	3.704/15	14.815/15	14.815/14	14.815/12	1.613/24	1.646/27	3.704/15	3.704/14
孝感	3.704/15	14.815/15	7.407/23	14.815/12	2.723/22	3.558/21	3.704/15	3.704/14
荆州	7.407/9	22.222/9	14.815/14	22.222/8	4.439/15	5.023/18	7.407/9	11.111/6
黄冈	3.704/15	14.815/15	11.111/20	18.519/11	0.400/28	1.356/28	3.704/15	3.704/14
咸宁	3.704/15	7.407/24	7.407/23	14.815/12	6.272/12	6.500/15	3.704/15	3.704/14
长沙	40.741/3	88.889/2	92.593/2	88.889/2	21.358/2	26.931/1	40.741/3	44.444/3
株洲	11.111/6	25.926/6	33.333/4	11.111/21	14.002/5	13.701/5	11.111/6	11.111/6
湘潭	25.926/4	11.111/19	14.815/14	11.111/21	5.007/14	7.117/13	25.926/4	18.519/4
衡阳	14.815/5	22.222/9	14.815/14	29.630/6	14.621/4	14.452/4	14.815/5	14.815/5
岳阳	11.111/6	18.519/12	7.407/23	25.926/7	10.014/7	10.324/9	11.111/6	7.407/10
常德	7.407/9	18.519/12	25.926/6	22.222/8	1.290/26	1.985/26	7.407/9	7.407/10
益阳	11.111/6	7.407/24	14.815/14	14.815/12	1.329/25	1.997/25	11.111/6	3.704/14
娄底	3.704/15	7.407/24	7.407/23	11.111/21	4.426/16	9.320/12	3.704/15	3.704/14
平均值	11.640	23.280	23.016	24.074	6.911	8.559	11.640	11.376
变异系数	1.341	0.938	0.989	0.969	0.843	0.784	1.341	1.373

Tab.3 Network degree centrality of urban agglomeration in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

城市	信息网络		经济网络		交通网络		创新网络
城市	2011年	2019年	2011年	2019年	2011年	2019年	2011年	2019年
南昌	44.444/2	59.259/3	55.556/3	66.667/3	14.879/3	19.596/3	44.444/2	48.148/2
景德镇	7.407/9	18.519/12	11.111/20	7.407/26	0.568/27	2.179/24	7.407/9	3.704/14
萍乡	3.704/15	14.815/15	22.222/8	7.407/26	8.840/8	12.104/6	3.704/15	3.704/14
九江	7.407/9	22.222/9	14.815/14	22.222/8	4.013/17	5.931/16	7.407/9	7.407/10
新余	3.704/15	11.111/19	25.926/6	3.704/28	8.337/9	9.961/10	3.704/15	3.704/14
鹰潭	3.704/15	7.407/24	3.704/28	11.111/21	10.040/6	12.092/7	3.704/15	0.000/28
吉安	7.407/9	11.111/19	22.222/8	14.815/12	2.658/23	2.735/23	7.407/9	3.704/14
宜春	3.704/15	25.926/6	18.519/10	14.815/12	7.291/11	9.949/11	3.704/15	3.704/14
抚州	3.704/15	11.111/19	11.111/20	11.111/21	3.342/19	4.369/20	3.704/15	11.111/6
上饶	3.704/15	25.926/6	18.519/10	14.815/12	8.220/10	11.874/8	3.704/15	3.704/14
武汉	70.370/1	92.593/1	96.296/1	100.000/1	21.771/1	24.861/2	70.370/1	66.667/1
黄石	3.704/15	11.111/19	18.519/10	14.815/12	3.239/20	5.217/17	3.704/15	3.704/14
宜昌	7.407/9	29.630/4	33.333/4	37.037/4	6.220/13	6.621/14	7.407/9	11.111/6
襄阳	3.704/15	29.630/4	18.519/10	33.333/5	3.394/18	3.256/22	3.704/15	7.407/10
鄂州	3.704/15	7.407/24	7.407/23	14.815/12	3.188/21	4.999/19	3.704/15	3.704/14
荆门	3.704/15	14.815/15	14.815/14	14.815/12	1.613/24	1.646/27	3.704/15	3.704/14
孝感	3.704/15	14.815/15	7.407/23	14.815/12	2.723/22	3.558/21	3.704/15	3.704/14
荆州	7.407/9	22.222/9	14.815/14	22.222/8	4.439/15	5.023/18	7.407/9	11.111/6
黄冈	3.704/15	14.815/15	11.111/20	18.519/11	0.400/28	1.356/28	3.704/15	3.704/14
咸宁	3.704/15	7.407/24	7.407/23	14.815/12	6.272/12	6.500/15	3.704/15	3.704/14
长沙	40.741/3	88.889/2	92.593/2	88.889/2	21.358/2	26.931/1	40.741/3	44.444/3
株洲	11.111/6	25.926/6	33.333/4	11.111/21	14.002/5	13.701/5	11.111/6	11.111/6
湘潭	25.926/4	11.111/19	14.815/14	11.111/21	5.007/14	7.117/13	25.926/4	18.519/4
衡阳	14.815/5	22.222/9	14.815/14	29.630/6	14.621/4	14.452/4	14.815/5	14.815/5
岳阳	11.111/6	18.519/12	7.407/23	25.926/7	10.014/7	10.324/9	11.111/6	7.407/10
常德	7.407/9	18.519/12	25.926/6	22.222/8	1.290/26	1.985/26	7.407/9	7.407/10
益阳	11.111/6	7.407/24	14.815/14	14.815/12	1.329/25	1.997/25	11.111/6	3.704/14
娄底	3.704/15	7.407/24	7.407/23	11.111/21	4.426/16	9.320/12	3.704/15	3.704/14
平均值	11.640	23.280	23.016	24.074	6.911	8.559	11.640	11.376
变异系数	1.341	0.938	0.989	0.969	0.843	0.784	1.341	1.373

Tab.4 Network intermediary centrality of urban agglomeration in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

城市	信息网络		经济网络		交通网络		创新网络
城市	2011年	2019年	2011年	2019年	2011年	2019年	2011年	2019年
南昌	17.489/2	12.097/3	7.716/3	11.562/3	11.854/3	7.044/1	42.308/2	39.934/2
景德镇	0.772/10	0.000/13	0.000/12	0.000/13	0.077/27	2.037/17	0.000/6	0.000/6
萍乡	0.214/19	0.000/13	0.000/12	0.000/13	3.609/12	1.748/18	0.000/6	0.000/6
九江	2.930/4	0.057/12	0.000/12	0.214/8	2.002/20	4.290/9	0.000/6	0.000/6
新余	0.321/18	0.000/13	0.214/8	0.000/13	3.609/12	1.748/18	0.000/6	0.000/6
鹰潭	0.000/22	0.000/13	0.000/12	0.000/13	8.163/5	5.404/5	0.000/6	0.000/6
吉安	0.000/22	0.000/13	0.000/12	0.000/13	4.474/9	3.863/12	0.000/6	0.000/6
宜春	0.497/15	0.625/8	0.071/9	0.000/13	3.609/12	1.748/18	0.000/6	0.000/6
抚州	0.000/22	0.000/13	0.000/12	0.000/13	4.382/11	2.106/16	0.000/6	0.000/6
上饶	0.973/9	2.032/4	7.502/4	0.095/10	5.238/7	4.714/7	0.000/6	0.000/6
武汉	26.548/1	37.987/1	37.749/1	40.997/1	14.47/1	7.044/1	60.351/1	52.374/1
黄石	0.460/16	0.214/11	0.071/9	0.000/13	0.780/23	0.692/26	0.000/6	0.000/6
宜昌	1.304/8	0.904/5	1.235/5	1.420/4	14.453/2	5.614/4	0.000/6	0.000/6
襄阳	0.621/13	0.904/5	0.071/9	0.897/6	10.110/4	3.900/11	0.000/6	0.000/6
鄂州	0.041/21	0.000/13	0.000/12	0.000/13	0.780/23	1.271/23	0.000/6	0.000/6
荆门	0.000/22	0.000/13	0.000/12	0.000/13	3.270/16	2.647/15	0.000/6	0.000/6
孝感	0.523/14	0.000/13	0.000/12	0.000/13	2.692/18	2.839/13	0.000/6	0.000/6
荆州	1.399/7	0.263/9	0.000/12	0.057/12	4.498/8	1.279/22	0.000/6	0.427/5
黄冈	1.456/6	0.000/13	0.000/12	0.071/11	0.071/28	0.241/28	0.000/6	0.000/6
咸宁	0.205/20	0.000/13	0.000/12	0.000/13	1.916/21	2.745/14	0.000/6	0.000/6
长沙	17.293/3	30.331/2	32.953/2	24.805/2	4.402/10	5.261/6	18.471/3	21.035/3
株洲	1.534/5	0.674/7	1.163/6	0.000/13	7.687/6	4.322/8	0.000/6	0.000/6
湘潭	0.686/11	0.000/13	0.000/12	0.000/13	2.347/19	0.808/24	5.271/4	0.760/4
衡阳	0.686/11	0.237/10	0.000/12	1.211/5	7.687/6	5.851/3	0.095/5	0.000/6
岳阳	0.404/17	0.000/13	0.000/12	0.294/7	1.916/21	4.282/10	0.000/6	0.000/6
常德	0.000/22	0.000/13	0.427/7	0.142/9	0.431/26	0.438/27	0.000/6	0.000/6
益阳	0.000/22	0.000/13	0.000/12	0.000/13	0.761/25	0.720/25	0.000/6	0.000/6
娄底	0.000/22	0.000/13	0.000/12	0.000/13	2.709/17	1.346/21	0.000/6	0.000/6
平均值	2.727	3.083	3.185	2.920	4.571	3.072	4.518	4.090
变异系数	2.364	2.961	2.927	3.088	0.893	0.665	3.081	3.090

Tab.4 Network intermediary centrality of urban agglomeration in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

城市	信息网络		经济网络		交通网络		创新网络
城市	2011年	2019年	2011年	2019年	2011年	2019年	2011年	2019年
南昌	17.489/2	12.097/3	7.716/3	11.562/3	11.854/3	7.044/1	42.308/2	39.934/2
景德镇	0.772/10	0.000/13	0.000/12	0.000/13	0.077/27	2.037/17	0.000/6	0.000/6
萍乡	0.214/19	0.000/13	0.000/12	0.000/13	3.609/12	1.748/18	0.000/6	0.000/6
九江	2.930/4	0.057/12	0.000/12	0.214/8	2.002/20	4.290/9	0.000/6	0.000/6
新余	0.321/18	0.000/13	0.214/8	0.000/13	3.609/12	1.748/18	0.000/6	0.000/6
鹰潭	0.000/22	0.000/13	0.000/12	0.000/13	8.163/5	5.404/5	0.000/6	0.000/6
吉安	0.000/22	0.000/13	0.000/12	0.000/13	4.474/9	3.863/12	0.000/6	0.000/6
宜春	0.497/15	0.625/8	0.071/9	0.000/13	3.609/12	1.748/18	0.000/6	0.000/6
抚州	0.000/22	0.000/13	0.000/12	0.000/13	4.382/11	2.106/16	0.000/6	0.000/6
上饶	0.973/9	2.032/4	7.502/4	0.095/10	5.238/7	4.714/7	0.000/6	0.000/6
武汉	26.548/1	37.987/1	37.749/1	40.997/1	14.47/1	7.044/1	60.351/1	52.374/1
黄石	0.460/16	0.214/11	0.071/9	0.000/13	0.780/23	0.692/26	0.000/6	0.000/6
宜昌	1.304/8	0.904/5	1.235/5	1.420/4	14.453/2	5.614/4	0.000/6	0.000/6
襄阳	0.621/13	0.904/5	0.071/9	0.897/6	10.110/4	3.900/11	0.000/6	0.000/6
鄂州	0.041/21	0.000/13	0.000/12	0.000/13	0.780/23	1.271/23	0.000/6	0.000/6
荆门	0.000/22	0.000/13	0.000/12	0.000/13	3.270/16	2.647/15	0.000/6	0.000/6
孝感	0.523/14	0.000/13	0.000/12	0.000/13	2.692/18	2.839/13	0.000/6	0.000/6
荆州	1.399/7	0.263/9	0.000/12	0.057/12	4.498/8	1.279/22	0.000/6	0.427/5
黄冈	1.456/6	0.000/13	0.000/12	0.071/11	0.071/28	0.241/28	0.000/6	0.000/6
咸宁	0.205/20	0.000/13	0.000/12	0.000/13	1.916/21	2.745/14	0.000/6	0.000/6
长沙	17.293/3	30.331/2	32.953/2	24.805/2	4.402/10	5.261/6	18.471/3	21.035/3
株洲	1.534/5	0.674/7	1.163/6	0.000/13	7.687/6	4.322/8	0.000/6	0.000/6
湘潭	0.686/11	0.000/13	0.000/12	0.000/13	2.347/19	0.808/24	5.271/4	0.760/4
衡阳	0.686/11	0.237/10	0.000/12	1.211/5	7.687/6	5.851/3	0.095/5	0.000/6
岳阳	0.404/17	0.000/13	0.000/12	0.294/7	1.916/21	4.282/10	0.000/6	0.000/6
常德	0.000/22	0.000/13	0.427/7	0.142/9	0.431/26	0.438/27	0.000/6	0.000/6
益阳	0.000/22	0.000/13	0.000/12	0.000/13	0.761/25	0.720/25	0.000/6	0.000/6
娄底	0.000/22	0.000/13	0.000/12	0.000/13	2.709/17	1.346/21	0.000/6	0.000/6
平均值	2.727	3.083	3.185	2.920	4.571	3.072	4.518	4.090
变异系数	2.364	2.961	2.927	3.088	0.893	0.665	3.081	3.090

Tab. 5 Subgroup of urban agglomeration network in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

凝聚子群	信息网络		经济网络
凝聚子群	2011年	2019年	2011年	2019年
子群一	南昌、景德镇、萍乡、九江、新余、鹰潭、吉安、宜春、抚州、上饶	景德镇、萍乡、九江、新余、鹰潭、吉安、宜春、抚州、上饶	南昌、景德镇、鹰潭	南昌、景德镇、鹰潭、孝感、鄂州、咸宁、九江、宜春、抚州、上饶、黄冈、黄石
子群二	株洲、湘潭、衡阳、常德、益阳、娄底	株洲、湘潭、衡阳、常德、益阳、娄底、岳阳、黄石、鄂州、咸宁	长沙、武汉	长沙、武汉
子群三	武汉、长沙、岳阳	南昌、长沙	宜昌、襄阳、荆门、孝感、荆州、常德、益阳、娄底、岳阳、鄂州、咸宁	宜昌、襄阳、荆门、荆州、常德、益阳、岳阳
子群四	黄石、宜昌、襄阳、鄂州、荆门、孝感、荆州、黄冈、咸宁	武汉、宜昌、襄阳、荆门、孝感、荆州、黄冈	萍乡、九江、新余、吉安、宜春、抚州、上饶、黄冈、株洲、湘潭、衡阳、黄石	娄底、萍乡、新余、吉安、株洲、湘潭、衡阳
凝聚子群	交通网络		创新网络
凝聚子群	2011年	2019年	2011年	2019年
子群一	南昌、景德镇、萍乡、九江、新余、鹰潭、吉安、宜春、抚州、上饶、娄底、湘潭	南昌、景德镇、抚州、九江、吉安	南昌、株洲、岳阳、湘潭、娄底、衡阳、常德、益阳	南昌、株洲、岳阳、湘潭、娄底、衡阳、常德、益阳、宜昌、荆州、抚州
子群二	长沙、株洲、衡阳	长沙、株洲、湘潭、娄底、新余、萍乡、宜春、鹰潭、上饶	孝感、鄂州、咸宁、黄冈、黄石、宜昌、襄阳、荆门、荆州	孝感、鄂州、咸宁、黄冈、黄石、襄阳、荆门
子群三	武汉、宜春、黄石、黄冈、荆州、鄂州	武汉、益阳、孝感、常德、襄阳、咸宁、岳阳、荆门、衡阳	景德镇、抚州、上饶、萍乡、鹰潭、九江、宜春、新余、吉安	景德镇、上饶、萍乡、九江、宜春、新余、吉安
子群四	咸宁、荆门、孝感、岳阳、常德、益阳、襄阳	黄冈、鄂州、黄石、宜春、荆州	武汉、长沙	武汉、长沙、鹰潭

Tab. 5 Subgroup of urban agglomeration network in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

凝聚子群	信息网络		经济网络
凝聚子群	2011年	2019年	2011年	2019年
子群一	南昌、景德镇、萍乡、九江、新余、鹰潭、吉安、宜春、抚州、上饶	景德镇、萍乡、九江、新余、鹰潭、吉安、宜春、抚州、上饶	南昌、景德镇、鹰潭	南昌、景德镇、鹰潭、孝感、鄂州、咸宁、九江、宜春、抚州、上饶、黄冈、黄石
子群二	株洲、湘潭、衡阳、常德、益阳、娄底	株洲、湘潭、衡阳、常德、益阳、娄底、岳阳、黄石、鄂州、咸宁	长沙、武汉	长沙、武汉
子群三	武汉、长沙、岳阳	南昌、长沙	宜昌、襄阳、荆门、孝感、荆州、常德、益阳、娄底、岳阳、鄂州、咸宁	宜昌、襄阳、荆门、荆州、常德、益阳、岳阳
子群四	黄石、宜昌、襄阳、鄂州、荆门、孝感、荆州、黄冈、咸宁	武汉、宜昌、襄阳、荆门、孝感、荆州、黄冈	萍乡、九江、新余、吉安、宜春、抚州、上饶、黄冈、株洲、湘潭、衡阳、黄石	娄底、萍乡、新余、吉安、株洲、湘潭、衡阳
凝聚子群	交通网络		创新网络
凝聚子群	2011年	2019年	2011年	2019年
子群一	南昌、景德镇、萍乡、九江、新余、鹰潭、吉安、宜春、抚州、上饶、娄底、湘潭	南昌、景德镇、抚州、九江、吉安	南昌、株洲、岳阳、湘潭、娄底、衡阳、常德、益阳	南昌、株洲、岳阳、湘潭、娄底、衡阳、常德、益阳、宜昌、荆州、抚州
子群二	长沙、株洲、衡阳	长沙、株洲、湘潭、娄底、新余、萍乡、宜春、鹰潭、上饶	孝感、鄂州、咸宁、黄冈、黄石、宜昌、襄阳、荆门、荆州	孝感、鄂州、咸宁、黄冈、黄石、襄阳、荆门
子群三	武汉、宜春、黄石、黄冈、荆州、鄂州	武汉、益阳、孝感、常德、襄阳、咸宁、岳阳、荆门、衡阳	景德镇、抚州、上饶、萍乡、鹰潭、九江、宜春、新余、吉安	景德镇、上饶、萍乡、九江、宜春、新余、吉安
子群四	咸宁、荆门、孝感、岳阳、常德、益阳、襄阳	黄冈、鄂州、黄石、宜春、荆州	武汉、长沙	武汉、长沙、鹰潭

Tab. 6 The density coefficient matrix of urban agglomeration network condensed subgroups in the middle reaches of the Yangtze River from the perspective of multi-source factor flow

凝聚子群		子群一	子群二	子群三	子群四
子群一	2011年	0.60/0.33/0.57/0.21	0.07/0.50/0.78/0.00	0.47/0.33/0.11/0.13	0.07/0.06/0.00/0.88
子群一	2019年	0.22/0.24/0.55/0.11	0.00/0.92/0.44/0.01	0.94/0.62/0.13/0.09	0.11/0.02/0.24/0.61
子群二	2011年	0.07/0.50/0.25/0.00	0.87/1.00/1.00/0.00	0.94/1.00/017/0.00	0.00/1.00/0.29/0.61
子群二	2019年	0.00/0.96/0.18/0.01	0.18/1.00/0.96/0.00	0.55/1.00/0.12/0.00	0.14/0.93/0.00/0.33
子群三	2011年	0.47/0.33/0.10/0.13	0.94/1.00/0.22/0.00	1.00/0.18/0.63/0.00	0.63/0.01/0.17/0.17
子群三	2019年	0.94/0.62/0.07/0.09	0.55/1.00/0.21/0.00	1.00/0.62/0.49/0.00	0.71/0.02/0.24/0.05
子群四	2011年	0.07/0.06/0.06/0.88	0.00/1.00/1.00/0.61	0.63/0.01/0.24/0.17	0.75/0.16/0.29/1.00
子群四	2019年	0.11/0.02/0.36/0.61	0.14/0.93/0.07/0.33	0.71/0.02/0.16/0.05	0.76/0.19/0.45/0.33

Tab.7 QAP correlation analysis of multiple urban networks in the middle reaches of the Yangtze River

多重网络		信息网络	经济网络	交通网络	创新网络
2011年	信息网络	—	0.739^***	0.672^***	0.773^***
	经济网络	0.739^***	—	0.576^***	0.739^***
	交通网络	0.672^***	0.576^***	—	0.640^***
	创新网络	0.773^***	0.739^***	0.640^***	—
2019年	信息网络	—	0.821^***	0.686^***	0.775^***
	经济网络	0.821^***	—	0.548^***	0.689^***
	交通网络	0.686^***	0.548^***	—	0.580^***
	创新网络	0.775^***	0.689^***	0.580^***	—

Tab. 8 Multiple network independent variable matrix in the middle reaches of the Yangtze River

矩阵	矩阵名称	矩阵内容
X₁	经济发展水平差异矩阵	城市人均GDP差值
X₂	就业规模差异矩阵	城市从业人口数量差值
X₃	政策干预差异矩阵	城市财政支出占GDP比重差值
X₄	产业结构差异矩阵	城市第二产业和第三产业占比差值
X₅	行政关系矩阵	同在一个省份为1，否则为0
X₆	可支配收入差距矩阵	城市人均可支配收入差值
X₇	空间邻近关系矩阵	空间邻近为1，否则为0

Tab.9 Regression results of multiple network influencing factors in the middle reaches of the Yangtze River

因素	2011年				2019年
因素	信息网络	经济网络	交通网络	创新网络	信息网络	经济网络	交通网络	创新网络
经济发展水平	0.029 8	0.065 3	0.158 1^**	0.052 7	0.166 3^**	0.097 2^*	0.230 3^***	0.099 9
就业规模	0.419 6^***	0.503 7^***	0.208 4^**	0.293 9^**	0.176 2	0.234 7	0.110 2	0.109 9
政策干预	－0.068 5^*	－0.142 6^**	－0.101 7^**	－0.088 0^**	－0.122 9^**	－0.050 5	－0.147 1^**	－0.117 7^**
产业结构	－0.047 6	－0.113 8^**	－0.200 7^***	－0.109 9^**	－0.016 2	－0.032 8	－0.162 8^**	－0.081 9
行政关系	0.449 7^***	0.046 6	0.230 1^***	0.168 4^**	0.273 3^***	0.069 3^*	0.245 9^***	0.088 5^*
收入差距	0.197 3^***	0.142 4^**	0.164 1^**	0.131 2^*	0.176 3	0.234 7	0.110 2	0.109 9
空间邻近	0.186 9^***	0.218 5^***	0.152 7^***	0.107 1^**	0.119 6^**	0.222 7^***	0.167 8^***	0.064 6^*
R²	0.362	0.357	0.268	0.103	0.617	0.445	0.277	0.212

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