Temporal network motif discovery method based on null model

doi:10.11772/j.issn.1001-9081.2022071033

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (8): 2505-2510.DOI: 10.11772/j.issn.1001-9081.2022071033

• Advanced computing • Previous Articles

Temporal network motif discovery method based on null model

Boren HU¹, Zhongmin PEI¹(), Zhangkai LUO¹, Jie DING²

^1.Key Laboratory of Complex Electronic System Simulation （Space Engineering University），Beijing 101416，China
^2.Department of Electronics and Optical Engineering，Space Engineering University，Beijing 101416，China

Received:2022-07-15 Revised:2022-10-12 Accepted:2022-10-13 Online:2023-01-04 Published:2023-08-10
Contact: Zhongmin PEI
About author:HU Boren， born in 1999， M. S. candidate. His research interests include network motif.
LUO Zhangkai， born in 1989， Ph. D， assistant research fellow. His research interests include communications and information systems， complex network.
DING Jie， born in 1998， M. S. candidate. Her research interests include communications and information systems.
Supported by:
Science and Technology on Complex Electronic System Simulation Laboratory Project(DXZT-JC-ZZ-2020-001)

基于零模型的含时网络模体识别方法

胡博仁¹, 裴忠民¹(), 罗章凯¹, 丁杰²

^1.复杂电子系统仿真重点实验室（航天工程大学），北京 101416
^2.航天工程大学电子与光学工程系，北京 101416

通讯作者: 裴忠民
作者简介:胡博仁（1999—），男，湖南宁乡人，硕士研究生，主要研究方向：网络模体
罗章凯（1989—），男，安徽滁州人，助理研究员，博士，主要研究方向：通信与信息系统、复杂网络
丁杰（1998—），女，安徽六安人，硕士研究生，主要研究方向：通信与信息系统。
基金资助:
复杂电子系统仿真重点实验室资助项目(DXZT?JC?ZZ?2020?001)

Abstract

Abstract:

In temporal networks with time attributes， conventional network motif discovery methods based on frequent subgraph statistics are easily affected by the differences in network size and structure. And an accurate benchmark for characteristic mining of empirical network can be provided by the null model network with same scale and some properties of the empirical network. Therefore， a temporal network motif discovery method based on null model was proposed to use relative values after comparing the features of the two network subgraphs to identify the subgraphs with significant structural meaning in temporal networks. At the same time， in order to determine when null model network reached stability， the method of successful scrambling times was adopted to improve the temporal network’s null model construction methods based on time scrambling or time randomization. In experiment stage， simulations were conducted on 46-node Global Positioning System （GPS） constellation containing satellites and ground stations， the number of successful scrambles times when the subgraph features of null model network reached stability was determined. Ten null model networks were constructed and compared with the satellite network. It was found that the number of occurrences of subgraph reflecting the continuity characteristics of node connection is only 1/34 of that of the subgraph with the highest frequency， but the former subgraph is the most important motif in the satellite network. Experimental results show that the temporal network’s motif discovery method with null model as reference can identify motifs that reflects network structural characteristics and dynamic change process more accurately.

Key words: temporal network, motif discovery, null model, successful scrambling times, satellite network

摘要：

在带有时间属性的含时网络中，常规的基于频繁子图统计的网络模体识别方法容易受网络规模与结构差异的影响。而与实证网络具有相同规模和某些相同性质的零模型网络能为实证网络的特性挖掘提供了准确的基准，于是提出一种基于零模型的含时网络模体识别方法，用两种网络子图特征比较后的相对值来识别含时网络中的具有显著结构意义的子图。同时，为确定零模型网络何时达到稳定，采用成功置乱次数方法来改进基于时间置乱或时间随机化的含时网络零模型构造方法。在实验阶段，对包含卫星和地面站的46节点全球定位系统（GPS）星座进行仿真实验，确定了零模型网络子图特征稳定时的成功置乱次数；构造10个零模型网络与卫星网络比较，发现反映节点连接具有连续性特点的子图的出现次数仅为最高频子图的1/34，却是卫星网络中最重要的模体。实验结果表明，以零模型为参照的含时网络模体识别方法能更准确地识别出反映网络结构特性和动态变化过程的模体。

关键词: 含时网络, 模体识别, 零模型, 成功置乱次数, 卫星网络

CLC Number:

TP393

Boren HU, Zhongmin PEI, Zhangkai LUO, Jie DING. Temporal network motif discovery method based on null model[J]. Journal of Computer Applications, 2023, 43(8): 2505-2510.

胡博仁, 裴忠民, 罗章凯, 丁杰. 基于零模型的含时网络模体识别方法[J]. 《计算机应用》唯一官方网站, 2023, 43(8): 2505-2510.

Figures/Tables 10

Fig. 1 Schematic diagram of time scrambling null model construction method

Fig. 2 Schematic diagram of time randomized null model construction method

Fig. 3 Flow of temporal network motif discovery method

Fig. 4 Subgraphs of temporal network constrained by δ

Fig. 5 Simulated weighted satellite network

Fig. 6 Schematic diagrams of 36 kinds of two-node three-side and three-node three-side directed subgraphs

Fig. 7 Occurrence frequency ratio of subgraph of original network to subgraph of time scrambling null model network

Fig. 8 Occurrence frequency ratio of subgraph of original network to subgraph of time randomized null model network

Tab. 1 Under the two null model construction algorithms， number of successful scrambling required for results to reach stability

子图	零模型构造算法		子图	零模型构造算法
子图	时间置乱	时间随机化	子图	时间置乱	时间随机化
M_5，6	0.3L	0.5L	M_6，2	0.5L	0.9L
M_4，2	0.4L	0.7L	M_6，1	0.6L	1.1L
M_6，6	0.4L	0.8L	M_4，6	0.2L	0.3L
M_5，1	0.4L	0.9L

Tab. 2 Statistical characteristics of subgraphs of time scrambling null model network

子图	原始网络中的出现次数	零模型网络中的平均出现次数	P	D	Z
M_5，6	1.51×N_5，6	N_5，6=9.57×10⁸	0	≤0.51	0.120
M_4，2	2.08×N_4，2	N_4，2=6.95×10⁸	0	≤1.08	0.156
M_6，6	2.22×N_6，6	N_6，6=4.12×10⁸	0	≤1.22	0.314
M_5，1	2.68×N_5，1	N_5，1=4.92×10⁷	0	≤1.68	0.431
M_6，2	2.95×N_6，2	N_6，2=2.98×10⁷	0	≤1.95	0.471
M_6，1	4.25×N_6，1	N_6，1=1.03×10⁷	0	≤3.25	0.574
M_4，6	0.22×N_4，6	N_4，6=2.82×10⁸	1	无	-0.354

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Temporal network motif discovery method based on null model

基于零模型的含时网络模体识别方法

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