The evolution and proximity mechanism of the innovation network of China's rare earth industry

doi:10.3969/j.issn.1004-9479.2026.02.20240521

Abstract

Abstract:

The spatial-temporal evolution characteristics of innovation network and its influence mechanism have become the focus of innovation economic geography, while the research on the dynamic evolution mechanism of industrial innovation network by internal and external factors urgently needs to be further deepened. Rare earth elements, often referred to as the "lifeline of high technology," play a crucial supporting role in technological innovation. This study analyzes the spatial structural evolution characteristics of China's rare earth industry innovation network, utilizing patent cooperation data from 2005 to 2021 and employing methodologies such as social network analysis and weighted index random graph models. It comprehensively explores the driving mechanisms of proximity, subject attributes, and endogenous dynamics in network evolution. The findings indicate that: ① The scale of China's rare earth industry innovation network continues to expand, with Beijing and Shanghai serving as core nodes, which catalyze the development of sub-core and peripheral cities, gradually forming a pyramid-like hierarchical network structure predominantly centered around eastern coastal cities; ② The network evolution demonstrates a transition from a "single-core multi-axis" structure to a "quadrilateral" model, characterized by a shift from core cities leading to a pattern where both core cities and regional centers drive development; ③ The evolution of the innovation network of China's rare earth industry is subjected to the common role of exogenous factors and endogenous momentum. Proximity dynamics and interactions play a role in different stages of innovation networks; cities with high innovation capacity promote network generation through 'strong alliances'; and the influence of path dependence gradually diminishes with the development of the industry.

Key words: internal and external factors, rare earth industry, innovation networks, evolutionary characteristics, influence mechanisms

摘要：

创新网络时空演化特征及其影响机制已成为创新经济地理学关注的焦点，而内外因素如何影响产业创新网络动态演化机制的研究亟须进一步深化。稀土作为“高科技的命脉”，对产业科技创新具有重要支撑作用。基于2005―2021年中国稀土产业合作专利数据，运用社会网络分析、加权指数随机图模型等方法，对中国稀土产业创新网络空间结构演化特征进行分析，系统探究邻近性、主体属性以及内生动力对网络演化的驱动机制。研究发现：①中国稀土产业创新网络规模持续扩大，以北京和上海为核心，带动次核心与边缘城市，逐步形成以东部沿海城市为主的“金字塔”形层级结构；②网络演化表现出从“单核多轴”向“四边形”格局转变，其特征表现为以点带面，由核心城市主导逐步向核心城市引领、区域中心带动的格局转变；③中国稀土产业创新网络的演化受到外生因素和内生动力的共同影响。邻近性在不同阶段的创新网络中产生动态交互作用；高创新能力城市通过“强强联合”推动网络的形成；路径依赖的约束作用随产业发展逐渐减弱。

关键词: 内外因素, 稀土产业, 创新网络, 演化特征, 影响机制

Yingmin HUANG, Qiang HUANG, Xiaohua ZOU, Xu ZHANG. The evolution and proximity mechanism of the innovation network of China's rare earth industry[J]. World Regional Studies, 2026, 35(2): 96-113.

黄颖敏, 黄蔷, 邹小华, 张旭. 中国稀土产业创新网络演化与影响机制[J]. 世界地理研究, 2026, 35(2): 96-113.

Figures/Tables 10

Fig.1 An explanatory framework for the impact mechanism of China's rare earth industry innovation network

Tab.1 Innovation network metrics and their implications

指标	表达式	解释
网络密度	$D = j n (n - 1) / 2$	表示网络各创新主体之间联系的紧密程度。j表示网络中实际存在的联系边的总数，n表示网络中城市节点的总数
平均路径长度	$L = ∑ j n d i j n (n - 1)$	表示整个网络节点间最短路径长度的平均值。d_ij 表示的是节点i与节点j之间的最短路径长度，n表示网络中节点的数量
集聚系数	$C = 1 n ∑ n 1 j i d i (d i - 1)$	表示网络中所有节点集聚系数的平均值，用于衡量创新网络中节点的结团程度。n表示节点数量， $j i$ 表示节点i与它自身邻接点间的边数； $d i$ 表示与i的邻接点的数量； $d i (d i - 1)$ 表示最大存在的可能边数
度中心度	$C C (i) = ∑ j = 1 n A i j$	表示网络中某一创新主体与其他创新主体相连的数量，用于衡量该节点与其他节点的直接联系程度。A_ij 表示节点i与节点j之间的总联系次数，n表示所有与节点i进行过直接合作的节点个数
中介中心度	$C B i = ∑ j n ∑ k n G j k i G j k$	表示某一节点在其他节点对的最短路径中充当桥梁作用的次数，用于衡量某一节点在网络中对资源控制的程度。j≠k≠i，且j＜k， $G j k$ 表示节点j 与节点k之间最短路径的数量
接近中心度	$C C (i) = 1 ∑ j ∈ N d i j$	表示的是某一节点在以距离为概念计算时的中心程度，用于衡量某一节点在网络中与其他节点的接近程度。 $d i j$ 表示节点i与节点j之间的距离

Tab.1 Innovation network metrics and their implications

指标	表达式	解释
网络密度	$D = j n (n - 1) / 2$	表示网络各创新主体之间联系的紧密程度。j表示网络中实际存在的联系边的总数，n表示网络中城市节点的总数
平均路径长度	$L = ∑ j n d i j n (n - 1)$	表示整个网络节点间最短路径长度的平均值。d_ij 表示的是节点i与节点j之间的最短路径长度，n表示网络中节点的数量
集聚系数	$C = 1 n ∑ n 1 j i d i (d i - 1)$	表示网络中所有节点集聚系数的平均值，用于衡量创新网络中节点的结团程度。n表示节点数量， $j i$ 表示节点i与它自身邻接点间的边数； $d i$ 表示与i的邻接点的数量； $d i (d i - 1)$ 表示最大存在的可能边数
度中心度	$C C (i) = ∑ j = 1 n A i j$	表示网络中某一创新主体与其他创新主体相连的数量，用于衡量该节点与其他节点的直接联系程度。A_ij 表示节点i与节点j之间的总联系次数，n表示所有与节点i进行过直接合作的节点个数
中介中心度	$C B i = ∑ j n ∑ k n G j k i G j k$	表示某一节点在其他节点对的最短路径中充当桥梁作用的次数，用于衡量某一节点在网络中对资源控制的程度。j≠k≠i，且j＜k， $G j k$ 表示节点j 与节点k之间最短路径的数量
接近中心度	$C C (i) = 1 ∑ j ∈ N d i j$	表示的是某一节点在以距离为概念计算时的中心程度，用于衡量某一节点在网络中与其他节点的接近程度。 $d i j$ 表示节点i与节点j之间的距离

Tab.2 Valued ERGMs model variables and indicators

变量	指标	解释	变量类型
多维邻近性	地理邻近性(Dis)	节点间欧氏距离	edgecov
	制度邻近性(Sis)	节点是否处在相同制度环境	edgecov
	社会邻近性(Soc)	节点间相对联系强度	edgecov
	认知邻近性(Int)	节点间技术相近程度	nodecov
	地理邻近性^认知邻近性(Dis^* Soc)*	地理邻近与认知邻近交互项	edgecov
	地理邻近性^社会邻近性(Dis^* Int)*	地理邻近与社会邻近交互项	edgecov
	地理邻近性^制度邻近性(Dis^* Sis)*	地理邻近与制度邻近交互项	edgecov
	认知邻近性^社会邻近性(Int^* Soc)*	认知邻近与社会邻近交互项	edgecov
	认知邻近性^制度邻近性(Int^* Sis)*	认知邻近与制度邻近交互项	edgecov
	社会邻近性^制度邻近性(Soc^* Sis)*	社会邻近与制度邻近交互项	edgecov
城市禀赋	行政等级(Adm)	主体的行政等级	nodefactor
	经济实力(Eco)	节点的年均生产总值	nodecov
	创新等级(Inn)	节点拥有的专利数量	nodecov
内生动力	传递效应(Tra)	是否倾向于形成三元包闭	transitiveweights
内生动力	择优链接(Pre)	是否更倾向与明星节点产生更多联系	edgecov

Tab.3 Rare earth industry chain division and patent search keywords

	关键词	补充分解
上游	稀土开采、稀土选矿、稀土矿石、稀土精矿、稀土冶炼、碳酸稀土、稀土化合物、稀土氧化物、稀土盐类、稀土金属等	氟碳铈矿、独居石、磷钇矿、风化壳淋积型矿、离子吸附型稀土等
中游	稀土永磁材料、稀土发光材料、稀土抛光材料、稀土储氢材料、稀土催化材料、稀土纳米材料等	钐钴永磁铁（SmCo5\sm2co17)、钕铁硼永磁铁(烧结钕铁硼、黏结钕铁硼、热压钕铁硼）、稀土铁氮性永磁铁、LaNi5型储氢合金(AB5型)、La-Mg-Ni系储氢合金(AB3型、A2B7型)、La2MgNi9、La5Mg2Ni23、La3MgNi14、La5Mg2Ni23合金、Mg-Ni-RE(RE=La,Nd) 系、Mg1.95Y0.05Ni0.92Al0.08、Mg35Ti10M5Ni50(M=Y、Al、Zr)、Ni Co Mg Al)5.1-xZnx(0.3≥x≥0,Ml代表富La混合稀土金属)等
下游	稀土应用	永磁电机、稀土、新能源汽车、稀土、尾气净化等

Fig.2 Changes in the number of rare earth invention patents in China from 2005 to 2021

Tab.4 Changing characteristics of China's rare earth industry innovation cooperation network from 2005 to 2021

阶段	网络规模			网络密度	集聚系数	网络中心势	平均路径长度/步
阶段	节点数/个	边数/个	直径/步	网络密度	集聚系数	网络中心势	平均路径长度/步
创新探索阶段	66	158	6	0.037	0.072	3.52%	2.641
创新追赶阶段	136	422	6	0.023	0.084	2.13%	2.957
创新突破阶段	167	696	6	0.025	0.131	2.06%	3.002

Tab.5 Evolution of the core-periphery cities of China's rare earth industry from 2005 to 2021

名称	核心城市	次级核心城市	边缘城市
创新探索阶段	北京、上海	抚顺、深圳	其余62个城市
创新追赶阶段	北京、上海	抚顺、深圳、天津、南京、大连、太原、广州	其余127个城市
创新突破阶段	北京、上海	大连、天津、廊坊、抚顺、石家庄、南京、合肥、保定、长沙、青岛、成都、苏州	其余141个城市

Tab.6 Evolution of the urban centrality of China's rare earth industry innovation network from 2005 to 2021

排名	创新探索阶段			创新追赶阶段			创新突破阶段
排名	度中心性	接近中心性	中介中心性	度中心性	接近中心性	中介中心性	度中心性	接近中心性	中介中心性
1	北京	北京	北京	北京	北京	北京	北京	北京	北京
	223	868	1 159	557	1 833	4 919	587	1 767	6 779
2	上海	上海	上海	上海	上海	上海	上海	上海	上海
	112	898	196	222	1 883	1 372	262	1 826	1 491
3	抚顺	杭州	长春	抚顺	广州	广州	大连	深圳	深圳
	38	904	160	155	1 901	1 189	108	1 836	1 426
4	扬州	长春	杭州	天津	武汉	杭州	深圳	南京	广州
	31	908	123	39	1 911	647	66	1 847	936
5	常州	武汉	武汉	深圳	杭州	深圳	南京	广州	长沙
	30	909	112	39	1 911	522	55	1 848	868
6	深圳	无锡	大连	广州	西安	武汉	天津	苏州	武汉
	18	910	83	32	1 913	514	52	1 856	836
7	长春	南京	天津	宁波	南京	南昌	武汉	杭州	南京
	16	910	54	29	1 916	452	51	1 861	831
8	杭州	大连	常州	南京	苏州	南京	佛山	合肥	杭州
	12	911	54	29	1 918	451	50	1 865	637
9	大连	天津	南京	杭州	无锡	苏州	廊坊	武汉	烟台
	11	911	54	27	1 919	408	38	1 866	630
10	天津	苏州	扬州	苏州	深圳	赣州	苏州	宁波	西安
	10	913	53	20	1 922	396	35	1 866	559

Fig. 3 Evolution of the spatial pattern of innovation network in China's rare earth industry

Tab.7 Fitting results of Valued ERGMs from China's rare earth industry innovation network

名称	变量	创新探索阶段（2005—2010）			创新追赶阶段（2011—2016）			创新突破阶段（2016—2021）
名称	变量	（1）	（2）	（3）	（4）	（5）	（6）	（7）	（8）	（9）
多维邻近性	B	0.419	0.057	-0.654	1.668^***	1.532^***	1.622^***	1.481^***	1.429^***	1.338^***
		(0.459)	(0.472)	(0.655)	(0.230)	(0.263)	(0.290)	(0.168)	(0.183)	(0.244)
	C	10.681^***	10.902^***	8.529^***	12.183^***	12.556^***	12.715^***	28.845^***	28.157^***	27.374^***
		(1.435)	(1.560)	(1.743)	(1.151)	(1.233)	(1.433)	(1.576)	(1.693)	(1.766)
	D	-0.693	-0.691	-0.330	0.142	0.150	0.434	-1.363^***	-1.314^***	-0.902^***
		(0.444)	(0.452)	(0.630)	(0.258)	(0.267)	(0.305)	(0.235)	(0.232)	(0.298)
	A*D		-0.029	-0.023		0.002	0.002		0.001	0.001
			(0.019)	(0.019)		(0.002)	(0.002)		(0.001)	(0.002)
	A*C		0.021	0.024		0.027	0.007		-0.076^*	-0.067
			(0.061)	(0.063)		(0.042)	(0.049)		(0.040)	(0.050)
	A*B		-0.015^**	-0.015^**		-0.002	-0.002		-0.001	-0.001
			(0.007)	(0.007)		(0.002)	(0.002)		(0.002)	(0.002)
	D*C			-1.370			-1.460^*			-1.364^*
				(0.906)			(0.773)			(0.703)
	D*B			0.320			-0.025			-0.050
				(0.269)			(0.082)			(0.063)
	C*B			2.808^**			-0.817			0.244
				(1.251)			(1.034)			(0.747)
城市禀赋	行政等级	-0.111	0.017	-0.012	0.230	0.224	0.197	0.333^***	0.336^***	0.339^***
	行政等级	(0.234)	(0.245)	(0.246)	(0.147)	(0.150)	(0.144)	(0.104)	(0.107)	(0.107)
	经济实力	1.158^**	1.180^**	1.271^**	0.159	0.188	0.257	2.192^***	2.161^***	2.234^***
	经济实力	(0.586)	(0.590)	(0.593)	(0.420)	(0.443)	(0.443)	(0.351)	(0.339)	(0.345)
	创新能力	13.719^***	13.808^***	13.783^***	19.400^***	19.305^***	18.953^***	8.479^***	8.467^***	7.864^***
	创新能力	(3.046)	(3.121)	(3.176)	(2.012)	(2.093)	(2.125)	(1.555)	(1.583)	(1.594)
内生动力	加权边	-6.443^***	-7.153^***	-7.335^***	-7.121^***	-7.117^***	-7.288^***	-6.211^***	-6.465^***	-6.590^***
	加权边	(0.464)	(0.608)	(0.632)	(0.270)	(0.297)	(0.306)	(0.181)	(0.223)	(0.236)
	传递效应	-0.644^***	-0.625^***	-0.595^***	-0.453^***	-0.448^***	-0.451^***	-0.181^**	-0.190^**	-0.179^**
	传递效应	(0.134)	(0.140)	(0.141)	(0.105)	(0.104)	(0.105)	(0.083)	(0.084)	(0.083)
	择优链接	-0.018^***	-0.018^***	-0.018^***	-0.014^***	-0.014^***	-0.014^***	-0.005^***	-0.005^***	-0.004^***
	择优链接	(0.005)	(0.005)	(0.005)	(0.002)	(0.002)	(0.002)	(0.001)	(0.001)	(0.001)
拟合度	AIC	-14025.923	-14120.629	-14032.773	-57721.538	-57800.263	-57697.376	-85276.394	-85694.206	-85278.875
拟合度	BIC	-13969.214	-14046.908	-13942.038	-57650.889	-57708.420	-57584.338	-85201.760	-85597.181	-85159.460

References 51

[1]	段德忠,杜德斌,谌颖,等.中国城市创新技术转移格局与影响因素.地理学报,2018,73(04):738-754.
	DUAN D, DU D, CHEN Y, et al. Technology transfer in China's city system: Process, pattern and influencing factors. Acta Geographica Sinica,2018,73(04):738-754.
[2]	刘承良,管明明,段德忠.中国城际技术转移网络的空间格局及影响因素.地理学报,2018,73(08):1462-1477.
	LIU C, GUAN M, DUAN D. Spatial pattern and influential mechanism of interurban technology transfer network in China. Acta Geographica Sinica, 2018, 73(08):1462-1477.
[3]	李琳,雒道政.多维邻近性与创新:西方研究回顾与展望.经济地理,2013,33(06):1-7.
	LI L, LUO D. Multi-proximity and innovation: The retrospect and prospect on western researches. Economic Geography, 2013, 33(06):1-7.
[4]	ROTHWELL R. Successful industrial innovation critical factors for the 1990s. Research and Development Management,1992, 22(3): 221-239.
[5]	FREEMAN C. Networks of innovators: A synthesis of research issues. Research Policy, 1991, 20(5): 499-514.
[6]	顾伟男,刘慧,王亮.国外创新网络演化机制研究.地理科学进展,2019,38(12):1977-1990.
	GU W, LIU H, WANG L.International research on the evolution mechanisms of innovation networks.Progress in Geography,2019,38(12):1977-1990.
[7]	周灿,曾刚,尚勇敏.演化经济地理学视角下创新网络研究进展与展望.经济地理,2019,39(05):27-36.
	ZHOU C, ZENG G, SHANG Y. Progress and prospect of research on innovation networks: A perspective from evolutionary economic geography. Economic Geography, 2019, 39(05):27-36.
[8]	马双,曾刚.网络视角下中国十大城市群区域创新模式研究.地理科学,2019,39(06):905-911.
	MA S, ZENG G. Regional innovation models of China's ten major urban agglomerations from the perspective of network. Scientia Geographica Sinica,2019, 39(06):905-911.
[9]	周锐波,刘叶子,杨卓文.中国城市创新能力的时空演化及溢出效应.经济地理,2019,39(04):85-92.
	ZHOU R, LIU Y, YANG Z. Spatial-temporal evolution and knowledge spillovers of urban innovation in China. Economic Geography, 2019, 39(04):85-92.
[10]	BOSCHMA R. Competitiveness of regions from an evolutionary perspective. Regional Studies, 2004, 38(9):1001-1014.
[11]	BOTTAZZI L, PERI G. Innovation and spillovers in regions: Evidence from European patent data. European Economic Review, 2003, 47(4): 687-710.
[12]	SHAW A, GILLY J. On the analytical dimension of proximity dynamics. Regional Studies, 2000, 34(2):169-180.
[13]	BUNNELL T, COE N. Spaces and scales of innovation. Progress in Human Geography, 2001, 25(4): 569-589.
[14]	BALLAND P, DEVAAN M, BOSCHMA R. The dynamics of interfirm networks along the industry life cycle: The case of the global video game industry, 1987-2007. Journal of Economic Geography, 2013, 13(5): 741-765.
[15]	曹贤忠,鲍涵,陈波,等.创新网络合作机制及其区域发展效应.世界地理研究,2024,33(07):150-159.
	CAO X, BAO H, CHEN B,et al.A review of the cooperation mechanism and regional development effect of innovation network, World Regional Studies, 2024,33(07):150-159.
[16]	刘炜,李郇,欧俏珊.产业集群的非正式联系及其对技术创新的影响——以顺德家电产业集群为例.地理研究,2013, 32(3):518-530.
	LIU W, LI X,OU Q. Informal ties in industrial cluster and its impact technological innovation:A case study of household appliance cluster in Shunde. Geographical Research, 2013, 32(3):518-530.
[17]	BALLAND P. Proximity and the evolution of collaboration networks:Evidence from research and development projects within the Global Navigation Satellite System(GNSS)industry. Regional Studies, 2012, 46(6):741-756.
[18]	范雅辰,曹卫东,陈枳宇,等.基于千强高新技术企业的中国城市创新网络研究.世界地理研究,2021,30(05):1036-1047.
	FAN Y, CAO W, CHEN Z, et al. Research on China's urban innovation network based on top 1000 high technology enterprises. World Regional Studies, 2021,30(05):1036-1047.
[19]	李二玲.中国农业产业集群演化过程及创新发展机制——以"寿光模式"蔬菜产业集群为例.地理科学, 2020, 40(4):617-627.
	LI E. The formation, evolution and innovative development of agricultural clusters in China:Case of the cluster nature of"Shouguang Mode". Scientia Geographica Sinica,2020,40(4):617-627.
[20]	香林,戴靓,朱禧惠,等.中国城市知识创新网络的等级性与区域性演化——以合著科研论文为例.现代城市研究,2021(01):25-31.
	XIANG L, DAI L, ZHU X,et al. Hierarchical and regional evolution of china's intercity knowledge innovation network: Evidence from scientific publication collaboration. Modern Urban Research, 2021(01):25-31.
[21]	张俊,姜海宁.合成型产业全球创新网络演化与邻近性机理:以节能环保产业为例.地理研究,2024,43(2):357-376.
	ZHANG J, JIANG H. Evolution of global innovation network and its proximity mechanism in synthetic industry: A case study of energy conservation and environmental protection industry. Geographical Research, 2024, 43(2):357-376.
[22]	WHITFIELD L, STARITZ C, MELESE A, et al. Technological capabilities, upgrading, and value capture in global value chains:Local apparel and floriculture firms in Sub-Saharan Africa. Economic Geography, 2020, 96(3):195-218.
[23]	VARGA A, SEBESTYÉN T, SZABÓN, et al. Estimating the economic impacts of knowledge network and entrepreneurship development in smart specialization policy. Regional Studies, 2020, 54(1):48-59.
[24]	戴靓,丁子军,马海涛,等.粤港澳大湾区技术转移的空间关联与内生动力.地理学报,2024,79(06):1503-1520.
	DAI L, DING Z, MA H,et al. Spatial linkages and endogenous mechanisms of technology transfer in the Guangdong-Hong Kong-Macao Greater Bay Area. Acta Geographica Sinica, 2024,79(06):1503-1520.
[25]	PAN Z. Varieties of intergovernmental organization memberships and structural effects in the world trade network.Advances in Complex Systems, 2018, 21(2):1850001.
[26]	曹贤忠,吕磊,曾刚.区域创新网络研究的重点领域及前沿方向.地域研究与开发,2023,42(4):1-6.
	CAO X,LYU L, ZENG G. Key areas and frontier directions of regional innovation network. Areal Research and Development, 2023,42(4):1-6.
[27]	索琪,李长升,王力媛.中国新能源汽车产业协同创新网络时空演化特征分析.世界地理研究,2024,33(02):79-92.
	SUO Q, LI C, WANG L. Spatio-temporal evolution characteristics of China's new energy vehicle industry collaborative innovation network. World Regional Studies, 2024,33(02):79-92.
[28]	刘通,毛炜圣,刘承良.长三角地区生物医药技术合作网络的空间演化及驱动机制.地理研究,2024,43(01):86-104.
	LIU T, MAO W, LIU C. The spatial pattern evolution and driving mechanism of the directed network of technological cooperation in the Yangtze River Delta. Geographical Research, 2024, 43(01):86-104.
[29]	王昶,刘雅琳,耿红军,等.基于P-TRM的中国稀土产业技术创新的政策演化路径研究.中南大学学报(社会科学版),2023,29(03):89-101.
	WANG C, LIU Y, GENG H, et al. Research on policy evolution path of technological innovation in China's rare earth industry based on Policy-Technology Roadmap, Journal of Central South University(Social Sciences), 2023,29(03):89-101.
[30]	周美静,黄健柏,邵留国,等.中国稀土政策演进逻辑与优化调整方向.资源科学,2020,42(08):1527-1539.
	ZHOU M, HUANG J, SHAO L, et al. Change and adjustment direction of China's rare earth policy, Resources Science, 2020,42(08):1527-1539.
[31]	李航飞,魏少彬.全球稀土贸易网络时空格局演化与中国地位变迁研究.世界地理研究,2024,33(6):1-13.
	LI H, WEI S. A study on spatial-temporal pattern evolution of global rare earth trade network and China's status change. World Regional Studies, 2024,33(6):1-13.
[32]	WANG X, YAO M, LI J, et al. Global embodied rare earths flows and the outflow paths of China's embodied rare earths: Combining multi-regional input-output analysis with the complex network approach. Journal of Cleaner Production, 2019, 216(APR.10):435-445.
[33]	夏启繁,杜德斌,段德忠,等.中国稀土对外贸易格局演化及影响因素.地理学报,2022,77(04):976-995.
	XIA Q, DU D, DUAN D,et al.Evolution and influencing factors of China's foreign trade in rare earth metals. Acta Geographica Sinica, 2022,77(04):976-995.
[34]	许振亮,陈子璇,于皓,等.国际稀土产业中游专利技术研发概况分析.科研管理,2020,41(12):43-59.
	XU Z, CHEN Z, YU H,et al. An analysis of the research and development of midstream patent technology of the international rare earth industry. Science Research Management, 2020,41(12):43-59.
[35]	DORIOMEDOV M, SEVASTYANOV D, SHEIN E. Technological, institutional and economic trends in the industry of rare and rare-earth metal. Proceedings of VIAM, 2019, 7(79): 3-11.
[36]	罗翔,赖丹.产业链延伸视角下稀土全产业链效率测度与比较研究:基于三阶段DEA模型.科学决策,2021(06):104-121.
	LUO X, LAI D. Measuring and comparing the efficiency of the whole industry chain of rare earths from the perspective of industry chain extension:Based on three-stage dea model. Scientific Decision Making, 2021(06):104-121.
[37]	王庆喜,胡志学.多维邻近下浙江城市创新网络演化及其机制研究.地理科学,2021,41(8):1380-1388.
	WANG Q, HU Z. Urban innovation network of zhejiang from the perspective of multidimensional proximities. Scientia Geographica Sinica, 2021, 41(8):1380-1388.
[38]	BOSCHMA R. Proximity and innovation: A critical assessment. Regional Studies, 2005, 39(1): 61-74.
[39]	MA H, WEI Y, DAI L, et al. The proximity and dynamics of intercity technology transfers in the Guangdong Hong Kong-Macau Greater Bay Area: Evidence from patent transfer networks. Environment and Planning A: Economy and Space, 2022,5 4(7): 1432-1449.
[40]	李冰,张纪海.军民科技创新合作网络结构与演化——基于专利合作与社会网络实证分析.科技进步与对策,2021,38(21):142-151.
	LI B, ZHANG J. The structure and evolution of military-civilian technological innovation cooperation network: An empirical analysis based on patent cooperation and social network. Science & Technology Progress and Policy, 2021,38(21):142-151.
[41]	MENZEL M, FORNAHL D. Cluster life cycles-dimensions and rationales of cluster evolution. Industrial and orporate Change, 2007, 19(1): 205 - 238.
[42]	桂钦昌,杜德斌,刘承良.全球科研合作网络的动态演化及其驱动机制.地理学报,2023,78(02):423-442.
	GUI Q, DU D, LIU C. The network dynamics and driving mechanisms of global scientific cooperation. Acta Geographica Sinica, 2023, 78(02):423-442.
[43]	VINCIGUERRA S, FRENKEN K, VALENTE M. The geography of internet infrastructure: An evolutionary simulation approach based on preferential attachment. Urban Studies, 2010, 47(9): 1969-1984.
[44]	KRIVITSKY P. Exponential-family random graph models for valued networks. Electronic Journal of Statistics, 2012, 6: 1100-1128.
[45]	PILNY A, ATOUBA Y. Modeling valued organizational communication networks using exponential random Graph Models. Management Communication Quarterly, 2018, 32(2): 250-264.
[46]	侯纯光,杜德斌,刘承良,等.全球留学生留学网络时空演化及其影响因素.地理学报,2020,75(4):681-694.
	HOU C, DU D, LIU C, et al. Spatio-temporal evolution and factors influencing international student mobility networks in the world. Acta Geographica Sinica, 2020,75(4):681-694.
[47]	GUI Q, LIU C, DU D. International knowledge flows and therole of proximity. Growth and Change, 2018, 49(3): 532-547.
[48]	JAFFE A, HENDERSON R, TRAJTENBERG M. Geographic localization of knowledge spillovers as evidenced by patent citations. Quaterly Journal of Economics, 1993, 108(3): 577-598.
[49]	曹湛,朱晟君,戴靓,等.多维邻近性对区域创新合作网络形成的影响——基于江浙沪医学科研机构的实证.地理研究,2022,41(9):2531-2547.
	CAO Z, ZHU S, DAI L, et al. The impact of multidimensional proximity on the formation of regional innovative collaboration network: A case study of medical science institutions in the Jiangsu-Zhejiang-Shanghai region. Geographical Research, 2022, 41(9):2531-2547.
[50]	罗翔,李政,赖丹.全球稀土新材料的技术演进及中国稀土产业链延伸的方向选择.有色金属科学与工程,2023,14(5):734-746.
	LUO X, LI Z, LAI D. Research on the technology evolution of global rare earth new materials and direction choice of China's rare earth industrial chain extension.Nonferrous Metals Science and Engineering,2023,14(5):734-746.
[51]	王蓓,刘卫东,陆大道.中国大都市区科技资源配置效率研究——以京津冀长三角和珠三角地区为例.地理科学进展,2011,30(10):1233-1239.
	WANG B, LIU W, LU D. Allocation efficiency of science and technology resources in Jing-Jin-Ji, Yangtze River Delta and Pearl River Delta Regions. Progress in Geography, 2011, 30(10):1233-1239.