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

Abstract

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

CLC Number:

TP 393

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

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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