基于弧有向加权时序网络超邻接矩阵列的节点重要性序结构演化辨识

doi:10.12305/j.issn.1001-506X.2026.03.22

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (3): 970-985.doi: 10.12305/j.issn.1001-506X.2026.03.22

• 系统工程 • 上一篇

基于弧有向加权时序网络超邻接矩阵列的节点重要性序结构演化辨识

胡钢¹^,²^,*, 康凯¹, 胡俊杰¹, 徐翔³, 任勇军⁴

1. 安徽工业大学管理科学与工程学院，安徽马鞍山 243032
2. 复杂系统多学科管理与控制安徽普通高校重点实验室，安徽马鞍山 243032
3. 国防科技大学信息系统工程重点实验室，湖南长沙 410073
4. 南京信息工程大学计算机学院，江苏南京 210044

收稿日期:2024-11-18 出版日期:2026-03-25 发布日期:2026-04-13
通讯作者: 胡钢
作者简介:康　凯（1998—），男，硕士研究生，主要研究方向为复杂网络系统建模仿真与均衡分析、多属性决策
胡俊杰（1999—），男，硕士研究生，主要研究方向为复杂网络系统建模仿真与均衡分析、多属性决策
徐　翔（1993—），男，博士研究生，主要研究方向为复杂网络系统建模仿真与均衡分析、供应链网络仿真与应用
任勇军（1974—），男，教授，博士，主要研究方向为区块链技术与数据安全
基金资助:
国家自然科学基金（62072249）；国家社会科学基金（19BGL254）；安徽省自然科学基金（2108085MG236）；安徽省高校自然科学研究项目（KJ2021A0385）资助课题

Identification of evolution of node importance order structure based on super-adjacency matrix columns of arc-directed weighted temporal networks

Gang HU¹^,²^,*, Kai KANG¹, Junjie HU¹, Xiang XU³, Yongjun REN⁴

1. School of Management Science and Engineering，Anhui University of Technology，Maanshan 243032，China
2. Key Laboratory of Multidisciplinary Management and Control of Complex Systems of Anhui Higher Education Institutes，Maanshan 243032，China
3. Science and Technology on Information Systems Engineering Laboratory，National University of Defense Technology，Changsha 410073，China
4. School of Computer Science，Nanjing University of Information Science and Technology，Nanjing 210044，China

Received:2024-11-18 Online:2026-03-25 Published:2026-04-13
Contact: Gang HU

摘要/Abstract

摘要：

弧有向加权时序网络可更加准确地描述节点间交互关联关系的倾向性选择及倾向性强度随时间演化过程中的变化，为辨识弧有向加权时序网络中的关键节点，提出基于多属性融合的弧有向加权时序网络节点重要性辨识方法。首先，为拓展挖掘网络时序演化多元信息源，集结网络多属性特征构建综合重要性矩阵列，可表征层内节点间交互关系的倾向性选择与倾向性强度大小。然后，定义节点层间传输能力相似度表征网络层间相似性。最后，融合节点间层内交互关系和层间关联关系构建弧有向加权时序网络多属性融合超邻接矩阵，并用特征向量列中心性方法对弧有向加权时序网络中的节点重要性排序，综合表征弧有向加权时序网络节点重要性序结构演化。实证数据仿真显示，所提模型对弧有向加权时序网络的关键特征有良好的表征，所得出的节点序结构在识别精度上优于其他模型，且排序靠前节点的传输能力优于其他模型。所提模型能为准确描述时序网络节点间复杂的交互关联关系提供思路，可为深入理解网络结构及其演化提供有力工具。

关键词: 有向加权时序网络, 超邻接时序矩阵列, 多属性融合, 序结构演化辨识

Abstract:

Arc-directed weighted temporal networks can more accurately describe the changing of the interactive association relationship of the tendency selection and intensity of tendency between nodes in the time-evolving. To identify key nodes in arc-directed weighted temporal networks, a method for assessing node importance based on multi-attribute fusion is proposed. Firstly, to expand and mine the temporal evolution of diverse information sources in networks, multi-attribute features of the network are aggregated to construct a comprehensive importance matrix column, which can represent the interactive association relationship of the tendency selection and intensity of tendency between the intra-layer nodes. Then, the similarity of transmission capabilities between node layers is defined to characterize the similarity between network layers. Finally, the multi-attribute fusion super-adjacency matrix of the arc-directed weighted temporal network is constructed by integrating the intra-layer interaction relationship and inter-layer association relationship between the nodes. The feature vector column centrality method is used to rank the importance of nodes in the arc-directed weighted temporal network, comprehensively characterizing the evolution of the node importance order structure in the arc-directed weighted temporal network. Empirical data simulation shows that the proposed model has a good representation of the key features of the arc-directed weighted temporal network, and the resulting node order structure has better recognition accuracy than other models, and the transmission capacity of the top ranked nodes is better than other models. The proposed model can provide ideas for accurately describing the complex interactive association relationships between nodes in temporal networks, and can provide powerful tools for a deeper understanding of network structure and its evolution.

Key words: directed weighted temporal network, super-adjacency temporal matrix column, multi-attribute fusion, order structure evolution and recognition

中图分类号:

TP 393

胡钢, 康凯, 胡俊杰, 徐翔, 任勇军. 基于弧有向加权时序网络超邻接矩阵列的节点重要性序结构演化辨识[J]. 系统工程与电子技术, 2026, 48(3): 970-985.

Gang HU, Kai KANG, Junjie HU, Xiang XU, Yongjun REN. Identification of evolution of node importance order structure based on super-adjacency matrix columns of arc-directed weighted temporal networks[J]. Systems Engineering and Electronics, 2026, 48(3): 970-985.

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数据集	节点数	交互次数	边数	时序片段/天	时间层数
Email-eu-core-temporal-Dept3	89	12 216	1 506	524	18
ia-radoslaw-email	167	82 927	22 902	271	14
Facebook-like Social Network	300	5 293	2 054	217	8

数据集	DWMASAM	文献[12]	文献[20]	文献[21]	文献[22]
Email-eu-core-temporal-Dept3	1	0.998 614	1	0.992 334	1
ia-radoslaw-email	0.999 857	0.998 575	0.999 857	0.990 118	0.999 857
Facebook-like Social Network	0.999 571	0.997 516	0.997 516	0.710 485	0.724 887

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基于弧有向加权时序网络超邻接矩阵列的节点重要性序结构演化辨识

Identification of evolution of node importance order structure based on super-adjacency matrix columns of arc-directed weighted temporal networks

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参考文献 32

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序号	Email-eu-core-temporal-Dept3					ia-radoslaw-email					Facebook-like Social Network
序号	本文方法	SAM	ISAM	SSAM	静态有向加权模型	本文方法	SAM	ISAM	SSAM	静态有向加权模型	本文方法	SAM	ISAM	SSAM	静态有向加权模型
1	25	60	60	25	54	38	38	38	38	38	9	103	9	44	9
2	49	25	25	60	25	45	45	7	45	3	282	9	8	51	36
3	60	49	49	49	49	7	7	27	7	18	8	176	63	56	44
4	16	16	16	16	48	27	27	70	27	15	177	41	44	62	63
5	35	54	54	54	16	70	70	94	70	50	288	32	34	68	32
6	54	23	35	35	43	94	94	1	94	13	109	36	52	59	72
7	80	35	48	23	23	1	1	68	1	59	175	58	6	20	19
8	48	48	30	48	60	68	68	90	68	1	97	101	12	32	6
9	85	30	23	1	85	90	90	69	90	86	127	8	69	36	34
10	1	88	43	14	14	69	69	9	69	9	142	63	73	58	12
11	43	43	80	30	35	9	9	18	18	94	299	114	50	48	3
12	23	80	14	77	26	18	18	50	9	54	212	277	36	34	27
13	14	14	77	88	71	50	50	59	50	42	27	44	58	72	1
14	11	77	24	85	4	59	59	42	59	68	101	67	67	6	67
15	30	24	1	43	80	42	42	13	42	14	144	97	48	3	30