In everyday life, we often observe unusually frequent interactions among people before or during important events, e.g., people send/receive more greetings to/from their friends on holidays than regular days. We also observe that some videos or hashtags suddenly go viral through people’s sharing on online social networks (OSNs). Do these seemingly different phenomena share a common structure? All these phenomena are associated with the sudden surges of node interactions in networks, which we call “bursts” in this work. We uncover that, in many scenarios, the emergence of a burst is accompanied with the formation of triangles in networks. This finding motivates us to propose a new and robust method for burst detection on an OSN. We first introduce a new measure, i.e., “triadic cardinality distribution,” corresponding to the fractions of nodes with different numbers of triangles, i.e., triadic cardinalities, in a network. We show that this distribution not only changes when a burst occurs, but it also has a robustness property that it is immunized against common spamming social-bot attacks. Hence, by tracking triadic cardinality distributions, we can more reliably detect bursts than simply counting node interactions on an OSN. To avoid handling massive activity data generated by OSN users during the triadic tracking, we design an efficient “sample-estimate” framework to provide maximum likelihood estimate of the triadic cardinality distribution. We propose several sampling methods and provide insights into their performance difference through both theoretical analysis and empirical experiments on real-world networks.

在日常生活中，我们经常观察到在重要事件发生之前或发生期间人们之间的异常频繁互动，例如，人们在节假日向朋友发送/从朋友那里收到的问候比平时多。我们还观察到某些视频或标签突然通过人们在在线社交网络（OSN）上的共享而传播开来。这些看似不同的现象是否具有相同的结构？所有这些现象都与网络中节点交互的突然激增有关，在这项工作中我们称之为“突发”。我们发现，在许多情况下，突发的出现伴随着网络中三角形的形成。这一发现促使我们提出了一种用于OSN上突发检测的新的健壮方法。我们首先介绍一项新措施，即““三元基数分布”，对应于网络中具有不同数量三角形的节点的分数，即三元基数。我们表明，这种分布不仅在发生爆发时发生变化，而且还具有健壮性，可以针对常见的垃圾邮件社交机器人攻击进行免疫。因此，通过跟踪三重基数分布，与简单地计算OSN上的节点交互作用相比，我们可以更可靠地检测突发。为了避免处理三方跟踪期间OSN用户生成的大量活动数据，我们设计了一种有效的“样本估算提供三元基数分布的最大似然估计的框架。我们提出了几种采样方法，并通过在现实世界网络上的理论分析和实证实验提供了它们的性能差异的见解。