This paper introduces graph-based mutually exciting processes (GB-MEP) to model event times in network point processes, focusing on an application to docked bike-sharing systems. GB-MEP incorporates known relationships between nodes in a graph within the intensity function of a node-based multivariate Hawkes process. This approach reduces the number of parameters to a quantity proportional to the number of nodes in the network, resulting in significant advantages for computational scalability when compared to traditional methods. The model is applied on event data observed on the Santander Cycles network in central London, demonstrating that exploiting network-wide information related to geographical location of the stations is beneficial to improve the performance of node-based models for applications in bike-sharing systems. The proposed GB-MEP framework is more generally applicable to any network point process where a distance function between nodes is available, demonstrating wider applicability.

翻译：本文提出基于图的互激过程（GB-MEP）用于对网络点过程中的事件时间建模，重点关注其在站点式共享单车系统中的应用。GB-MEP将图中节点间的已知关系融入基于节点的多元霍克斯过程的强度函数中。该方法将参数数量减少至与网络节点数成比例的量，相较于传统方法在计算可扩展性上具有显著优势。该模型应用于伦敦市中心桑坦德自行车网络观测到的事件数据，结果表明利用与站点地理位置相关的全网信息，有助于提升基于节点模型在共享单车系统应用中的性能。所提出的GB-MEP框架更广泛地适用于任何存在节点间距离函数的网络点过程，展现出较强的普适性。