多层网络中一致的强三元封闭性

Lutz Oettershagen, Athanasios L. Konstantinidis, Fariba Ranjbar, Giuseppe F. Italiano
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引用次数: 0

摘要

社交网络用户通常会与数百甚至数千名其他用户建立联系。推断联系强度是社交网络分析中的一项重要任务。常见的方法是根据当时的网络拓扑结构,使用强三元闭合(STC)将联系分为强边和弱边。STC 指出,对于 $\textit{A}$、$\textit{B}$ 和 $\textit{C}$这三个节点,如果 $\textit{A}$ 和 $\textit{B}$,以及 $\textit{A}$ 和 $\textit{C}$之间存在强联系,那么 $\textit{B}$ 和 $\textit{C}$ 之间必然存在(弱或强)联系。此外,被称为 STC+ 的 STC 变体允许添加新的弱连接来获得更好的解。最近,社交网络分析的重点已经从单层网络转向了多层网络,这是因为多层网络能够代表多个社交网络平台(如 Facebook、LinkedIn 或 X(原 Twitter))中具有多种类型交互或关系的复杂系统。然而,直接将 STC 分别应用于多层网络的每一层通常会导致层与层之间的标签不一致。避免这种不一致是非常重要的,因为它们与领带强度代表了用户之间关系的基本、一致的事实这一观点相矛盾。因此,我们为多层网络调整了 STC 和 STC+ 的定义,并提供了精确解决问题的 ILP 公式。求解 ILPs 的计算成本很高;因此,我们另外为 STC 和 STC+ 的最小化变体提供了高效的 2 近似值和 6 近似值。实验表明,与标准方法不同,我们的新高效算法能为多层网络边缘带来一致的强/弱标记。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Consistent Strong Triadic Closure in Multilayer Networks
Social network users are commonly connected to hundreds or even thousands of other users. However, these ties are not all of equal strength; for example, we often are connected to good friends or family members as well as acquaintances. Inferring the tie strengths is an essential task in social network analysis. Common approaches classify the ties into strong and weak edges based on the network topology using the strong triadic closure (STC). The STC states that if for three nodes, $\textit{A}$, $\textit{B}$, and $\textit{C}$, there are strong ties between $\textit{A}$ and $\textit{B}$, as well as $\textit{A}$ and $\textit{C}$, there has to be a (weak or strong) tie between $\textit{B}$ and $\textit{C}$. Moreover, a variant of the STC called STC+ allows adding new weak edges to obtain improved solutions. Recently, the focus of social network analysis has been shifting from single-layer to multilayer networks due to their ability to represent complex systems with multiple types of interactions or relationships in multiple social network platforms like Facebook, LinkedIn, or X (formerly Twitter). However, straightforwardly applying the STC separately to each layer of multilayer networks usually leads to inconsistent labelings between layers. Avoiding such inconsistencies is essential as they contradict the idea that tie strengths represent underlying, consistent truths about the relationships between users. Therefore, we adapt the definitions of the STC and STC+ for multilayer networks and provide ILP formulations to solve the problems exactly. Solving the ILPs is computationally costly; hence, we additionally provide an efficient 2-approximation for the STC and a 6-approximation for the STC+ minimization variants. The experiments show that, unlike standard approaches, our new highly efficient algorithms lead to consistent strong/weak labelings of the multilayer network edges.
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