Link prediction is an elemental issue for network-structured data mining, which has already found a wide range of applications. The organization of real-world networks usually embodies both regularities and irregularities, and the precision of link prediction algorithms coincides with the portion of a network being categorized as regular. Quantifying and controlling how well an unobserved link can be predicted is a fundamental problem in link prediction. This paper proposes a structural regularity-exploring architecture, called NetSRE, for measuring and regulating link predictability of networks. The proposed NetSRE assumes that there are consistent interaction patterns across the local subgraphs of networks and one of them can be represented by a linear summation of the others, and thus, link predictability can be characterized by the self-representation degree of network structures. Specifically, NetSRE includes (1) a low Frobenius norm pursuit-based self-representation network model for predicting the “true” underlying networks, (2) a “structural regularity” index for measuring the link predictability of networks, i.e., the inherent difficulty of link prediction independent of specific algorithms, and (3) an importance measuring method for structural role exploration of network links and a link-based structure perturbation algorithm for link predictability regulation. Experimental results on real-world networks validate the performance of our method. It is found that real-world networks have various structural regularities and link predictability can be estimated based on structure mining directly. We show that network heterogeneity provides a way to intrinsically segregate network links into qualitatively distinct groups, which have different influences on the link predictability of networks.

链接预测是网络结构数据挖掘的一个基本问题，已经发现了广泛的应用。实际网络的组织通常包含规则性和不规则性，并且链接预测算法的精度与网络中被归类为常规的部分一致。量化和控制如何预测未观察到的链路是链路预测中的一个基本问题。本文提出了一种结构规则性探索架构，称为NetSRE，用于测量和调节网络的链路可预测性。提出的NetSRE假设网络的局部子图之间存在一致的交互模式，并且其中一个可以用其他线性图的线性求和来表示，因此，链路可预测性可以通过网络结构的自表示程度来表征。具体来说，NetSRE包括（1）用于预测“真实”基础网络的基于Frobenius范式的低自表示网络模型，（2）用于测量网络链路可预测性（即固有难度）的“结构规则性”指标独立于特定算法的链路预测的原理；（3）用于网络链路结构角色探索的重要性度量方法和用于链路可预测性调节的基于链路的结构摄动算法。实际网络上的实验结果验证了我们方法的性能。发现现实世界的网络具有各种结构规律性，并且可以直接基于结构挖掘来估计链接的可预测性。