Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, and so on. This article summaries recent progress about link prediction algorithms, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods. We also introduce three typical applications: reconstruction of networks, evaluation of network evolving mechanism and classification of partially labelled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.

Abstract. Missing link prediction of networks is of both theoretical interest and practical significance in modern science. In this paper, we empirically investigate a simple framework of link prediction on the basis of node similarity. We compare nine well-known local similarity measures on six real networks. The results indicate that the simplest measure, namely Common Neighbors, has the best overall performance, and the Adamic-Adar index performs the second best. A new similarity measure, motivated by the resource allocation process taking place on networks, is proposed and shown to have higher prediction accuracy than common neighbors. It is found that many links are assigned same scores if only the information of the nearest neighbors is used. We therefore design another new measure exploited information of the next nearest neighbors, which can remarkably enhance the prediction accuracy.PACS. 89.75.-k Complex systems -05.65.+b Self-organized systems

The one-mode projecting is extensively used to compress the bipartite networks. Since the onemode projection is always less informative than the bipartite representation, a proper weighting method is required to better retain the original information. In this article, inspired by the networkbased resource-allocation dynamics, we raise a weighting method, which can be directly applied in extracting the hidden information of networks, with remarkably better performance than the widely used global ranking method as well as collaborative filtering. This work not only provides a creditable method in compressing bipartite networks, but also highlights a possible way for the better solution of a long-standing challenge in modern information science: How to do personal recommendation?

Recommender systems use data on past user preferences to predict possible future likes and interests. A key challenge is that while the most useful individual recommendations are to be found among diverse niche objects, the most reliably accurate results are obtained by methods that recommend objects based on user or object similarity. In this paper we introduce a new algorithm specifically to address the challenge of diversity and show how it can be used to resolve this apparent dilemma when combined in an elegant hybrid with an accuracy-focused algorithm. By tuning the hybrid appropriately we are able to obtain, without relying on any semantic or context-specific information, simultaneous gains in both accuracy and diversity of recommendations.etting what you want, as the saying goes, is easy; the hard part is working out what it is that you want in the first place (1). Whereas information filtering tools like search engines typically require the user to specify in advance what they are looking for (2-5), this challenge of identifying user needs is the domain of recommender systems (5-8), which attempt to anticipate future likes and interests by mining data on past user activities.Many diverse recommendation techniques have been developed, including collaborative filtering (6, 9), content-based analysis (10), spectral analysis (11, 12), latent semantic models and Dirichlet allocation (13,14), and iterative self-consistent refinement (15-17). What most have in common is that they are based on similarity, either of users or objects or both: for example, e-commerce sites such as Amazon.com use the overlap between customers' past purchases and browsing activity to recommend products (18,19), while the TiVo digital video system recommends TV shows and movies on the basis of correlations in users' viewing patterns and ratings (20). The risk of such an approach is that, with recommendations based on overlap rather than difference, more and more users will be exposed to a narrowing band of popular objects, while niche items that might be very relevant will be overlooked.The focus on similarity is compounded by the metrics used to assess recommendation performance. A typical method of comparison is to consider an algorithm's accuracy in reproducing known user opinions that have been removed from a test dataset. An accurate recommendation, however, is not necessarily a useful one: real value is found in the ability to suggest objects users would not readily discover for themselves, that is, in the novelty and diversity of recommendation (21). Despite this, most studies of recommender systems focus overwhelmingly on accuracy as the only important factor [for example, the Netflix Prize (22) challenged researchers to increase accuracy without any reference to novelty or personalization of results]. Where diversification is addressed, it is typically as an adjunct to the main recommendation process, based on restrictive features such as semantic or other context-specific information (23, 24).The clear concern is that an alg...

Real networks exhibit heterogeneous nature with nodes playing far different roles in structure and function. To identify vital nodes is thus very significant, allowing us to control the outbreak of epidemics, to conduct advertisements for e-commercial products, to predict popular scientific publications, and so on. The vital nodes identification attracts increasing attentions from both computer science and physical societies, with algorithms ranging from simply counting the immediate neighbors to complicated machine learning and message passing approaches. In this review, we clarify the concepts and metrics, classify the problems and methods, as well as review the important progresses and describe the state of the art. Furthermore, we provide extensive empirical analyses to compare well-known methods on disparate real networks, and highlight the future directions. In despite of the emphasis on physics-rooted approaches, the unification of the language and comparison with cross-domain methods would trigger interdisciplinary solutions in the near future.

Identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance. The degree centrality method is very simple but of little relevance. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but are incapable to be applied in large-scale networks due to the computational complexity. In order to design an effective ranking method, we proposed a semi-local centrality measure as a tradeoff between the low-relevant degree centrality and other time-consuming measures. We use the Susceptible-Infected-Recovered (SIR) model to evaluate the performance by using the spreading rate and the number of infected nodes. Simulations on four real networks show that our method can well identify influential nodes.

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has a great scientific depth and combines diverse research fields which makes it of interests for physicists as well as interdisciplinary researchers.

We propose a routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called efficient path, which considers the possible congestion in the nodes along actual paths. Since the nodes with the largest degree are very susceptible to traffic congestion, an effective way to improve traffic and control congestion, as our strategy, can be redistributing traffic load in central nodes to other noncentral nodes. Simulation results indicate that the network capability in processing traffic is improved more than 10 times by optimizing the efficient path, which is in good agreement with the analysis.