## PUBLICATION

- Looking into Complex Networks (in Chinese) 总结了几位作者对复杂网络研究中存在的重要问题和发展趋势的讨论，其中既包括度分布和度指数的分析和计算，各种不同动力学之间的内在一致性，网络加速增长机制这样的基本问题，也包括了网络中尺度这类细致深入的结构分析 还就复杂网络与其他重要研究方向深入结合的现状和未来展开了讨论，包括复杂网络中的链路预测问题，复杂网络在信息推荐系统中的应用，复杂网络与信息物理系统的可能结合，复杂网络和人类动力学的结合以及复杂网络在国家安全方面可能的重要战略地位。 - L. Lü, J.-A. Lu, Z.-K. Zhang, X.-Y. Yan, Y. Wu, D.-H. Shi, H.-P. Zhou, J.-Q. Fang, T. Zhou - Complex Systems and Complexity Science 7(2-3), 173 (2010) - PDF

- Empirical comparision of local structural similarity indices for collaborative-filtering-based recommender systems Collaborative filtering is one of the most successful recommendation techniques, which can effectively predict the possible future likes of users based on their past preferences. The key problem of this method is how to define the similarity between users. A standard approach is using the correlation between the ratings that two users give to a set of objects, such as Cosine index and Pearson correlation coefficient. However, the costs of computing this kind of indices are relatively high, and thus it is impossible to be applied in the huge-size systems. To solve this problem, in this paper, we introduce six local-structure-based similarity indices and compare their performances with the above two benchmark indices. Experimental results on two data sets demonstrate that the structure-based similarity indices overall outperform thePearson correla-tion coefficient. When the data is dense, the structure-based indices can perform competitively good asCosine index, while with lower computational complexity. Furthermore, when the data is sparse, the structure-based indices give even better results thanCosine index. - Q.-M Zhang, M.-S. Shang, W. Zeng, Y. Chen, L. Lü* - Physics Procedia 3, 1887 (2010) - PDF

- Can Dissimilar Users Contribute to Accuracy and Diversity of Personalized Recommendation? Recommender systems are becoming a popular and important set of personalization techniques that assist individual users with navigating through the rapidly growing amount of information. A good recommender system should be able to not only nd out the objects preferred by users, but also help users in discovering their personalized tastes. The former corresponds to high accuracy of the recommendation, while the latter to high diversity . A big challenge is to design an algorithm that provides both highly accurate and diverse recommendation. Traditional recommendation algorithms only take into account the contributions of similar users, thus, they tend to recommend popular items for users ignoring the diversity of recommendations. In this paper, we propose a recommendation algorithm by considering both the eects of similar and dissimilar users under the framework of collaborative ltering. Extensive analyses on three datasets, namely MovieLens, Netflix and Amazon, show that our method performs much better than the standard collaborative ltering algorithm for both accuracy and diversity . - W. Zeng, M.-S. Shang, Q.-M. Zhang, L. Lü*, T. Zhou - Int. J. Mod. Phys. C 21, 1217 (2010) - PDF

- Similarity-Based Classification in Partially Labeled Networks We propose a similarity-based method, using the similarity between nodes, to ad-dress the problem of classification in partially labeled networks. The basic assump-tion is that two nodes are more likely to be categorized into the same class if they are more similar. In this paper, we introduce ten similarity indices, including five local ones and five global ones. Empirical results on the co-purchase network of political books show that the similarity-based method can give high accurate clas-sification even when the labeled nodes are sparse which is one of the difficulties in classification. Furthermore, we find that when the target network has many labeled nodes, the local indices can perform as good as those global indices do, while when the data is spares the global indices perform better. Besides, the similarity-based method can to some extent overcome the unconsistency problem which is another difficulty in classification. - Q.-M. Zhang, M.-S. Shang, L. Lü* - Int. J. Mod. Phys. C 21, 813 (2010) - PDF

- Empirical analysis of web-based user-object bipartite networks Understanding the structure and evolution of web-based user-object networks is a significant task since they play a crucial role in e-commerce nowadays. This Letter reports the empirical analysis on two large-scale web sites, audioscrobbler.com and del.icio.us, where users are connected with music groups and bookmarks, respectively. The degree distributions and degree-degree correlations for both users and objects are reported. We propose a new index, named collaborative clustering coefficient, to quantify the clustering behavior based on the collaborative selection. Accordingly, the clustering properties and clustering-degree correlations are investi-gated. We report some novel phenomena well characterizing the selection mechanism of web users and outline the relevance of these phenomena to the information recommendation problem. - M.-S. Shang, L. Lü, Y.-C. Zhang, T. Zhou - EPL 90, 48006 (2010) - PDF

- Zipf’s Law Leads to Heaps’ Law: Analyzing Their Relation in Finite-Size Systems Background:Zipf’s law and Heaps’ law are observed in disparate complex systems. Of particular interests, these two laws often appear together. Many theoretical models and analyses are performed to understand their co-occurrence in real systems, but it still lacks a clear picture about their relation. Methodology/Principal Findings:We show that the Heaps’ law can be considered as a derivative phenomenon if the system obeys the Zipf’s law. Furthermore, we refine the known approximate solution of the Heaps’ exponent provided the Zipf’s exponent. We show that the approximate solution is indeed an asymptotic solution for infinite systems, while in the finite-size system the Heaps’ exponent is sensitive to the system size. Extensive empirical analysis on tens of disparate systems demonstrates that our refined results can better capture the relation between the Zipf’s and Heaps’ exponents. Conclusions/Significance:The present analysis provides a clear picture about the relation between the Zipf’s law and Heaps’ law without the help of any specific stochastic model, namely the Heaps’ law is indeed a derivative phenomenon from the Zipf’s law. The presented numerical method gives considerably better estimation of the Heaps’ exponent given the Zipf’s exponent and the system size. Our analysis provides some insights and implications of real complex systems. For example, one can naturally obtained a better explanation of the accelerated growth of scale-free networks. - L. Lü, Z.-K. Zhang, T. Zhou - PLoS ONE 5(12), e14139 (2010) - PDF

- 复杂网络链路预测 网络中的链路预测是指如何通过已知的网络结构等信息预测网络中尚未产生连边的两个节点之间产生连接的可能性。预测那些已经存在但尚未被我们发现的连接实际上是一种数据挖掘的过程，而对于未来可能产生的连边的预测则与网络的演化相关。传统的方法是基于马尔科夫链或者机器学习的，往往考虑节点的属性特征。这类方法虽然能够得到较高的预测精度，但是由于计算的复杂度以及非普适性的参数使其应用范围受到限制。另一类方法是基于网络结构的最大似然估计，这类方也有计算复杂度高的问题。相比上述两种方法，基于网络结构相似性的方法更加简单。通过在多个实际网络中的实验发现，基于相似性的方法能够得到很好的预测效果，并且网络的拓扑结构性质能够帮助选择合适的相似性指标。本文综述并比较了若干有代表性的链路预测方法，展望了若干重要的开放性问题，可望为相关学者提供借鉴。 - 吕琳媛 - 电子科大学报, 39 (2010) 651 - PDF

- Link prediction in weighted networks: the role of weak ties Plenty of algorithms for link prediction have been proposed and were applied to various real networks. Among these algorithms, the weights of links are rarely taken into account. In this letter, we use local similarity indices to estimate the likelihood of the existence of links in weighted networks, includingCommon Neighbor, Adamic-Adar Index, Resource Allocation Index, and their weighted versions. We have tested the prediction accuracy on real social, technological and biological networks. Overall speaking, the resource allocation index performs best. To our surprise, sometimes the weighted indices perform even worse than the unweighted indices, which reminds us of the well-known Weak-Ties Theory. Further experimental study shows that the weak ties play a significant role in the link prediction, and to emphasize the contributions of weak ties can remarkably enhance the prediction accuracy for some networks. We give asemi-quantitative explanation based on the motif analysis. This letter provides a start point for the possible weak-ties theory in information retrieval. - Linyuan Lü and Tao Zhou - Europhys. Lett. 89 (2010) 18001 - PDF

- Link prediction based on local random walk The problem of missing link prediction in complex networks has attracted much attention recently. Two difficulties in link prediction are the sparsity and huge size of the target networks. Therefore, the design of an efficient and effective method is of both theoretical interests and practical significance. In this Letter, we proposed a method based on local random walk, which can give competitively good prediction or even better prediction than other random-walk-based methods while has a lower computational complexity - WeiPing Liu, and Linyuan Lü - Europhys. Lett. 89 (2010) 58007. - PDF