Linyuan Lü

Link prediction in complex networks: A survey

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 labeled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.

Similarity index based on local paths for link prediction of complex networks

Predictions of missing links of incomplete networks like protein-protein interaction networks or very likely but not yet existent links in evolutionary networks like friendship networks in web society can be considered as a guideline for further experiments or valuable information for web users. In this paper, we introduce a local path index to estimate the likelihood of the existence of a link between two nodes. We propose a network model with controllable density and noise strength in generating links, as well as collect data of six real networks. Extensive numerical simulations on both modeled networks and real networks demonstrated the high effectiveness and efficiency of the local path index compared with two well-known and widely used indices, the common neighbors and the Katz index. Indeed, the local path index provides competitively accurate predictions as the Katz index while requires much less CPU time and memory space, which is therefore a strong candidate for potential practical applications in data mining of huge-size networks.

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, to design an efficient and effective method is of both theoretical interest and practical significance. In this letter, we proposed a method based on local random walk, which can give competitively good or even better prediction than other random-walk–based methods while having a much lower computational complexity.

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, including Common 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 a semi-quantitative explanation based on the motif analysis. This letter provides a start point for the possible weak-ties theory in information retrieval.

Vital nodes identification in complex networks

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.

The small world yields the most effective information spreading

Spreading dynamics of information and diseases are usually analyzed by using a unified framework and analogous models. In this paper, we propose a model to emphasize the essential difference between information spreading and epidemic spreading, where the memory effects, the social reinforcement and the non-redundancy of contacts are taken into account. Under certain conditions, the information spreads faster and broader in regular networks than in random networks, which to some extent supports the recent experimental observation of spreading in online society [D. Centola, Science {\bf 329}, 1194 (2010)]. At the same time, simulation result indicates that the random networks tend to be favorable for effective spreading when the network size increases. This challenges the validity of the above-mentioned experiment for large-scale systems. More significantly, we show that the spreading effectiveness can be sharply enhanced by introducing a little randomness into the regular structure, namely the small-world networks yield the most effective information spreading. Our work provides insights to the understanding of the role of local clustering in information spreading.

Toward link predictability of complex networks

Significance Quantifying a networks link predictability allows us to (i) evaluate predictive algorithms associated with the network, (ii) estimate the extent to which the organization of the network is explicable, and (iii) monitor sudden mechanistic changes during the networks evolution. The hypothesis of this paper is that a group of links is predictable if removing them has only a small effect on the networks structural features. We introduce a quantitative index for measuring link predictability and an algorithm that outperforms state-of-the-art link prediction methods in both accuracy and universality. This study provides fundamental insights into important scientific problems and will aid in the development of information filtering technologies. The organization of real networks usually embodies both regularities and irregularities, and, in principle, the former can be modeled. The extent to which the formation of a network can be explained coincides with our ability to predict missing links. To understand network organization, we should be able to estimate link predictability. We assume that the regularity of a network is reflected in the consistency of structural features before and after a random removal of a small set of links. Based on the perturbation of the adjacency matrix, we propose a universal structural consistency index that is free of prior knowledge of network organization. Extensive experiments on disparate real-world networks demonstrate that (i) structural consistency is a good estimation of link predictability and (ii) a derivative algorithm outperforms state-of-the-art link prediction methods in both accuracy and robustness. This analysis has further applications in evaluating link prediction algorithms and monitoring sudden changes in evolving network mechanisms. It will provide unique fundamental insights into the above-mentioned academic research fields, and will foster the development of advanced information filtering technologies of interest to information technology practitioners.

The H-index of a network node and its relation to degree and coreness.

Identifying influential nodes in dynamical processes is crucial in understanding network structure and function. Degree, H-index and coreness are widely used metrics, but previously treated as unrelated. Here we show their relation by constructing an operator , in terms of which degree, H-index and coreness are the initial, intermediate and steady states of the sequences, respectively. We obtain a family of H-indices that can be used to measure a nodes importance. We also prove that the convergence to coreness can be guaranteed even under an asynchronous updating process, allowing a decentralized local method of calculating a nodes coreness in large-scale evolving networks. Numerical analyses of the susceptible-infected-removed spreading dynamics on disparate real networks suggest that the H-index is a good tradeoff that in many cases can better quantify node influence than either degree or coreness.

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 similarity, to quantify the diversity of tastes based on the collaborative selection. Accordingly, the correlation between degree and selection diversity is investigated. 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.

Identifying Influential Spreaders by Weighted LeaderRank

Identifying influential spreaders is crucial for understanding and controlling spreading processes on social networks. Via assigning degree-dependent weights onto links associated with the ground node, we proposed a variant to a recent ranking algorithm named LeaderRank (Lu et al., 2011). According to the simulations on the standard SIR model, the weighted LeaderRank performs better than LeaderRank in three aspects: (i) the ability to find out more influential spreaders; (ii) the higher tolerance to noisy data; and (iii) the higher robustness to intentional attacks.