In this study, a temporal graph model is designed to model the behavior of collective sports teams based on the networks of player interactions. The main motivation for the model is to integrate the temporal dimension into the analysis of players' passing networks in order to gain deeper insights into the dynamics of system behavior, particularly how a system exploits the degeneracy property to self-regulate. First, the temporal graph model and the entropy measures used to assess the complexity of the dynamics of the network structure are introduced and illustrated. Second, an experiment using basketball data is conducted to investigate the relationship between the complexity level and team performance. This is accomplished by examining the correlations between the entropy measures in a team's behavior and the team's final performance, as well as the link between the relative score compared to that of the opponent and the entropy in the team's behavior. Results indicate positive correlations between entropy measures and final team performance, and threshold values of relative score associated with changes in team behavior -- thereby revealing common and unique team signatures. From a complexity science perspective, the model proves useful for identifying key performance factors in team sports and for studying the effects of given constraints on the exploitation of degeneracy to organize team behavior through various network structures. Future research can easily extend the model and apply it to other types of social networks.

中文翻译：

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研究团队运动中集体行为和表现动态的时间图模型：在篮球中的应用

在本研究中，设计了一个时间图模型来根据玩家交互网络对集体运动队的行为进行建模。该模型的主要动机是将时间维度整合到玩家传球网络的分析中，以便更深入地了解系统行为的动态，特别是系统如何利用简并属性进行自我调节。首先，介绍并说明了用于评估网络结构动态复杂性的时间图模型和熵度量。其次，使用篮球数据进行实验来研究复杂性水平与团队绩效之间的关系。这是通过检查团队行为的熵度量与团队最终表现之间的相关性，以及与对手相比的相对得分与团队行为的熵之间的联系来实现的。结果表明，熵度量与最终团队绩效以及与团队行为变化相关的相对分数阈值之间存在正相关性，从而揭示了共同和独特的团队特征。从复杂性科学的角度来看，该模型对于识别团队运动中的关键绩效因素以及研究给定约束对利用简并性通过各种网络结构组织团队行为的影响非常有用。未来的研究可以轻松扩展该模型并将其应用于其他类型的社交网络。