为识别有向加权网络中的重要加权模体,采用边权定性为强弱标签的方式将有向加权网络转换为标签网络、简单模体拓展至标签模体。对于三节点的标签模体类型,用模体在随机网络中出现相应次数的概率估计值代替模体遍历的含时过程,引入与标签模体类型相关联的动态指标识别出有向加权网络中的重要标签模体。将其应用到中国篮球职业联赛(CBA)2019—2020赛季总决赛广东队、辽宁队的传球网络,获得球队在比赛中出现的重要传球模式及构成相应传球模式的重要球员。重要标签模体的识别对挖掘有向加权网络的重要构建模式、关键节点有着显著作用。
In order to identify the important weighted motifs in the directed weighted networks, the directed weighted networks are transformed into label networks and the simple motifs are expanded to label motifs by defining the edge weights as strong and weak labels. For the label motifs of the three nodes, the time-consuming procedure of subgraph traversal is replaced by the estimated probability of the corresponding number of the motifs appear in the random networks, and the important label motifs in the directed weighted networks are identified by introducing a dynamic indicator associated with the label motif type. It is applied to the passing networks of Guangdong team and Liaoning team in the 2019—2020 finals of China Basketball Association (CBA). The important passing modes of the teams in the games and the important players in the corresponding modes are obtained. The important label motifs play a significant role in mining the important construction patterns and key nodes of the directed weighted networks.
[1]MILO R, SHEN-ORR S, ITZKOVITZ S, et al. Network motifs: simple building blocks of complex networks[J]. Science, 2002, 298(5594): 824-827.
[2]SPORNS O, KÖTTER R, FRISTON K J. Motifs in brain networks[J]. PLoS Biology, 2004, 2(11): e369.
[3]BENSON A R, GLEICH D F, LESKOVEC J. Higher-order organization of complex networks[J]. Science, 2016, 353(6295): 163-166.
[4]SHEN-ORR S S, MILO R, MANGAN S, et al. Network motifs in the transcriptional regulation network of Escherichia coli[J]. Nature Genetics, 2002, 31(1): 64-68.
[5]DOBRIN R, BEG Q K, BARABÁSI A L, et al. Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network[J]. BMC Bioinformatics, 2004, 5(1): 1-8.
[6]JIN Y, WEI Y, XIU C, et al. Study on structural characteristics of China′s passenger airline network based on network motifs analysis[J]. Sustainability, 2019, 11(9): 2484.
[7]贾承丰, 韩华, 完颜娟, 等. 基于网络模体特征攻击的网络抗毁性研究[J]. 复杂系统与复杂性科学, 2019, 14(4): 43-50.
JIA C F, HAN H, WAN Y J, et al. Network destruction resistance based on network motif feature[J]. Complex Systems and Complexity Science, 2019, 14(4): 43-50.
[8]LIU H, XU X, LU J A, et al. Optimizing pinning control of complex dynamical networks based on spectral properties of grounded Laplacian matrices[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 51(2): 786-796.
[9]刘慧, 王炳珺, 陆君安, 等. 复杂网络牵制控制优化选点算法及节点组重要性排序[J]. 物理学报, 2021, 70(5): 284.
LIU H, WANG B J, LU J A, et al. Node-set importance and optimization algorithm of nodes selection in complex networks based on pinning control[J]. Acta Physica Sinica, 2021, 70(5): 284.
[10] ONNELA J P, SARAMÄKI J, KERTÉSZ J, et al. Intensity and coherence of motifs in weighted complex networks[J]. Physical Review E, 2005, 71(6): 065103.
[11] CHOOBDAR S, RIBEIRO P, SILVA F. Motif mining in weighted networks[C]∥2012 IEEE 12th International Conference on Data Mining Workshops. Brussels, Belgium: IEEE, 2012: 210-217.
[12] LI J, YANG D, JI C. Mine weighted network motifs via Bayes′ Theorem[C]∥2017 4th International Conference on Systems and Informatics (ICSAI). Hangzhou, China: IEEE, 2017: 448-452.
[13] LI J, LV P, JI C. Uncover product review patterns via weighted motifs[C]∥2018 5th International Conference on Systems and Informatics (ICSAI). Nanjing, China: IEEE, 2018: 445-448.
[14] LI J, YANG D, LV P. Visualize classic play′s composing patterns: a weighted motif mining framework[J]. Multimedia Tools and Applications, 2019, 78(5): 5989-6012.
[15] SHEN X, GONG X, JIANG X, et al. High-order organization of weighted microbial interaction network[C]//2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). Madrid, Spain: IEEE, 2018: 206-209.
[16] PICCIOLO F, RUZZENENTI F, HOLME P, et al. Weighted network motifs as random walk patterns[J]. New Journal of Physics, 2022, 24(5): 053056.
[17] 张岩, 杨改生. 社会网络分析在团队运动表现中的应用:研究综述[J]. 中国体育科技, 2022, 58(1): 100-108.
ZHANG Y, YANG G S. The application of social network analysis in team sports performance:a review[J]. China Sport Science and Technology, 2022, 58(1): 100-108.
[18] HÅLAND E M, WIIG A S, HVATTUM L M, et al. Evaluating the effectiveness of different network flow motifs in association football[J]. Journal of Quantitative Analysis in Sports, 2020, 16(4): 311-323.
[19] ÇOBANOGˇLU H O. Using of network motifs on basketball tactical analysis[J]. Journal of Education and Training Studies, 2019, 7(3S): 62-70.
[20] PICARD F, DAUDIN J J, KOSKAS M, et al. Assessing the exceptionality of network motifs[J]. Journal of Computational Biology, 2008, 15(1): 1-20.
