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Very large-scale social networks are typically sparse and dynamic and often have millions of nodes and billions of links. Link prediction in very large-scale networks is a challenging task for most existing methods. This paper investigates the link prediction problem in very large-scale networks. We propose a model, namely, a very large-scale network co-occurrence embedding algorithm (Hsem), which learns the co-occurrence features of node pairs to embed nodes into a vector with a lower and fixed dimension. A damping-based random walk algorithm is also developed to extract the hierarchical structural information of node pairs. Moreover, we design an incremental learning algorithm based on Hsem to meet the requirements of highly dynamic evolution in very large-scale networks, which significantly improves learning speed while maintaining accuracy. Finally, we present controlled experiments employing the proposed and baseline methods on eight challenging real-world large-scale datasets with a fixed dropout percentage and calculate the time overhead and receiver operating characteristics. The results show that Hsem performs comparably to current state-of-the-art methods and consistently outperforms the baselines in different experimental settings. [ABSTRACT FROM AUTHOR]

Given the edge list of a social network, the node embedding method learns the structural features for every node and embeds the features into a vector space. The current related work on node embedding exploits only a portion of existing networks, e.g., static networks. However, social networks are inherently hierarchical and dynamic systems in which the topology changes constantly and the strength of influence of information among neighbors varies with different numbers of hops. We propose a highly efficient node embedding method, Dnps, that is faster and more accurate than state-of-the-art methods and that can further boost the training progress, especially under dynamic conditions. In this paper, we attempt to model the hierarchical and dynamic features of social networks by designing a damping-based sampling algorithm corresponding to a local search-based incremental learning algorithm, which can easily be extended to large-scale scenarios. We conduct extensive experiments on six real-world social networks with three challenging tasks, including missing link prediction, dynamic link prediction, and multi-label classification. The results of the experiments on these tasks demonstrate that the proposed method significantly outperforms the existing methods with different settings. [ABSTRACT FROM AUTHOR]

Most of the current studies on social network (SN) mainly focused on a single SN platform. Integration of SNs can provide more sufficient user behaviour data and more complete network structure, and thus is rewarding to an ocean of studies on social computing. Recognizing the identical users across SNs, or user identification, naturally bridges the SNs through users and has attracted extensive attentions. Due to the fragmentation, inconsistency and disruption of the accessible information among SNs, user identification is still an intractable problem. Different from the efforts implemented on user profiles and users' content, many studies have noticed the accessibility and reliability of network structure in most of the SNs for addressing this issue. Although substantial achievements have been made, most of the current network structure-based solutions are supervised or semi-supervised and require some given identified users or seed users. In the scenarios where seed users are hard to obtain, it is laborious to label the seed users manually. In this study, we proposed an unsupervised scheme by employing the reliability and consistence of friend relationships in different SNs, termed Unsupervised Friend Relationship-based User Identification algorithm (UFRUI). The UFRUI first models the network structure and embeds the feature of each user into a vector using network embedding technique, and then converts the user identification problem into a nearest neighbour problem. Finally, the matching user is computed using the scalable nearest neighbour algorithm. Results of experiments demonstrated that UFRUI performs much better than current state-of-art network structure-based algorithm without seed users. [ABSTRACT FROM AUTHOR]

Online social networks have continued to attract increased attention since the introduction of this concept nearly three decades ago. Consequently, a study about the workings of online social networks may help in understanding the structure of human society and the characteristics of generic complex networks. Over the past few years, interest in neighboring nodes, which are the number of nodes between any two nodes, the number of neighbors and how many triangles are present in a social network have produced the concepts of a six-degree separation (Milgram, Psychol Today 2(1):60–67, 1967; Backstrom et al., Proceedings of the 4th annual ACM web science conference, p 33–42, 2012), a heavy tail in the degree distribution (Barabási, Albert, Science 286(5439):509–512, 1999) and a high clustering coefficient (Luce, Perry, Psychometrika 14(2):95–116, 1949; Watts, Strogatz, Nature 393(6684):440–442, 1998; Amaral et al., Proc Natl Acad Sci USA 97(21):11149–11152, 2000). In a similar manner, researchers have also been curious about how many polygons are present in a given online social network. Although much effort has been expended (Dantzig et al., International symposium on theory of graphs, p 77–83, 1967; Kamae, IEEE Trans Circuit Theory 14(2):166–171, 1967; Gotlieb, Corneil, Commun ACM 10(12):780–783, 1967; Welch, J ACM 13(2):205–210, 1966; Tiernan, Commun ACM 13(12):722–726, 1970; Tarjan, SIAM J Comput 2(3):211–216, 1973; Johnson, SIAM J Comput 4:77–84, 1975; Mateti, Deo, SIAM J Comput 5(5):90–99, 1976; Marinari et al., Europhys Lett 73(3):301–307, 2005), studying this subject, the inability to enumerate polygons has stymied an in depth understanding of the properties of polygons in an online social network. In the study described in this paper, the estimated number of polygons in an online social network is revealed. It was found that in the current widely used online social networks, e.g., Facebook, Twitter, the number of polygons increases drastically when the length of a polygon is below a set value and then it decreases rapidly. The average length of the network polygons was calculated and it was found that online social networks contain a relatively large average length of polygons. Based on this perspective, a massive labyrinth of polygons would make the online social networks appear to be very complicated. To further investigate this area, a generalized clustering coefficient was explored. Results showed that the generalized clustering coefficient appeared to descend exponentially with the length of polygon and expeditiously approached zero. This result suggested that the polygons with large lengths should be ignored in many scenarios. Since the polygons with lengths greater than five appeared to have little impact on the network, the online social networks appeared to be less complex than anticipated. The polygon is one of the fundamental problems in graph theory and complex networks, so that the work reported here may be beneficial for many disciplines, including transportation [7], engineering [8], computer science [9–16], physics (Birmelé et al., Proceedings of the 24th annual ACM–SIAM symposium on discrete algorithms, p 1884–1896, 2013), sociology (Motter, Albert, Phys Today 65:43, 2012), epidemiology (Feld, Am J Sociol 96(6):1464–1477, 1991; Cohen et al., Phys Rev Lett 91(24):12343, 2002), psychology (Sun et al., Sci Rep 4(6188):5099–5099, 2014), biology (Feiler, Kleinbaum, Psychol Sci, 2015), medicine (Kincaid, Pilette, Comput Appl Biosci Cabios 8:267–273, 1992), geography (Kim et al., Lancet 386(9989):145–153, 2015), etc. [ABSTRACT FROM AUTHOR]