Link-prediction is an active research field within network theory, aiming at uncovering missing connections or predicting the emergence of future relationships from the observed network structure. This paper represents our contribution to the stream of research concerning missing links prediction. Here, we propose an entropy-based method to predict a given percentage of missing links, by identifying them with the most probable non-observed ones. The probability coefficients are computed by solving opportunely defined null-models over the accessible network structure. Upon comparing our likelihood-based, local method with the most popular algorithms over a set of economic, financial and food networks, we find ours to perform best, as pointed out by a number of statistical indicators (e.g. the precision, the area under the ROC curve, etc.). Moreover, the entropy-based formalism adopted in the present paper allows us to straightforwardly extend the link-prediction exercise to directed networks as well, thus overcoming one of the main limitations of current algorithms. The higher accuracy achievable by employing these methods - together with their larger flexibility - makes them strong competitors of available link-prediction algorithms.
为了评估丢失链接预测的性能，已知数据被随机分为两部分，训练集和探测集。我们认为，这种直接和标准的方法可能会导致可怕的偏见，因为在真实的生物和信息网络中，丢失的链接更有可能是连接低度节点的链接。因此，我们研究如何发现丢失的链接与低度节点，即在探针集的链接是较低的度产品比随机抽样。对10个局部相似性指数和4个不同的真实网络的实验分析表明，Leicht-Holme-Newman指数[E. A. Leicht，P. Holme，and M. E. J. Newman，Phys.Rev.E73，026120（2006）]表现最好，尽管已知如果探测集是所有链路的随机采样，则它是最差的索引之一。我们进一步提出了一个参数依赖的指数，这大大提高了预测精度。最后，我们展示了三种真实抽样方法的相关性。
Missing links prediction: comparing machine learning with physics-rooted approaches
IMT School for Advanced Studies（IMT高等研究院）；Department of Physics and INFN, ‘Tor Vergata’ University of Rome（罗马托尔维加塔大学物理系及意大利国家核物理研究所）；Scuola Normale Superiore（比萨高等师范学院）；INdAM-GNAMPA Istituto Nazionale di Alta Matematica ‘Francesco Severi’（弗朗切斯科·塞韦里国家高等数学研究所）
Entropy-based link prediction in weighted networks
信息熵已被证明是量化复杂网络结构重要性的有效工具。在之前的工作中（Xu et al，2016 \cite{xu2016}），我们用信息熵来衡量路径在链接预测中的贡献。本文进一步用路径熵和路径权重来量化路径的贡献，并提出一种基于路径贡献的加权预测指标--加权路径熵（WPE），以提高加权网络的预测精度。在六个加权真实网络上的实验表明，WPE比三个典型的加权指数具有更高的预测精度。
