Social networks often provide only a binary perspective on social ties: two individuals are either connected or not. While sometimes external information can be used to infer the strength of social ties, access to such information may be restricted or impractical to obtain. Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging the Strong Triadic Closure (STC) property. The STC property states that if person A has strong social ties with persons B and C, B and C must be connected to each other as well (whether with a weak or strong tie). They exploited this property to formulate the inference of the strength of social ties as a NP-hard maximization problem, and proposed two approximation algorithms. We refine and improve this line of work, by developing a sequence of linear relaxations of the problem, which can be solved exactly in polynomial time. Usefully, these relaxations infer more fine-grained levels of tie strength (beyond strong and weak), which also allows one to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. Moreover, these relaxations allow us to easily change the objective function to more sensible alternatives, instead of simply maximizing the number of strong edges. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, while at the same time questioning the validity of leveraging the STC property for edge strength inference in practice.

中文翻译：

---

放宽强三合子闭合问题以进行边缘强度推断

社交网络通常仅提供关于社交关系的二元观点：两个人之间是否有联系。尽管有时可以使用外部信息来推断社会联系的强度，但是获取此类信息可能受到限制或不切实际。Sintos和Tsaparas（KDD 2014）首先建议通过利用强三合会封闭（STC）属性从网络拓扑推断社会关系的强度。STC财产规定，如果人A与人B和C有牢固的社会联系，则B和C必须彼此连接（无论是弱领带还是强领带）。他们利用这一特性将对社会纽带强度的推论公式化为一个N​​P硬最大化问题，并提出了两种近似算法。我们通过开发问题的线性松弛序列来完善和改进这一工作范围，可以在多项式时间内准确地解决该问题。有用的是，这些松弛可以推断出连接强度的更细粒度级别（强和弱之外），这也可以避免在网络拓扑提供不确定的证据时进行任意的强/弱强度分配。而且，这些放宽使我们能够轻松地将目标函数更改为更明智的选择，而不是简单地最大化强边的数量。广泛的理论分析导致两种有效的算法方法。最后，我们的实验结果阐明了所提出方法的优势，同时在实践中质疑了利用STC属性进行边缘强度推断的有效性。