Spreading predictability in complex networks.

Many state-of-the-art researches focus on predicting infection scale or threshold in infectious diseases or rumor and give the vaccination strategies correspondingly. In these works, most of them assume that the infection probability and initially infected individuals are known at the very beginning. Generally, infectious diseases or rumor has been spreading for some time when it is noticed. How to predict which individuals will be infected in the future only by knowing the current snapshot becomes a key issue in infectious diseases or rumor control. In this report, a prediction model based on snapshot is presented to predict the potentially infected individuals in the future, not just the macro scale of infection. Experimental results on synthetic and real networks demonstrate that the infected individuals predicted by the model have good consistency with the actual infected ones based on simulations.

Identifying critical nodes in temporal networks by network embedding.

Critical nodes in temporal networks play more significant role than other nodes on the structure and function of networks. The research on identifying critical nodes in temporal networks has attracted much attention since the real-world systems can be illustrated more accurately by temporal networks than static networks. Considering the topological information of networks, the algorithm MLI based on network embedding and machine learning are proposed in this paper. we convert the critical node identification problem in temporal networks into regression problem by the algorithm. The effectiveness of proposed methods is evaluated by SIR model and compared with well-known existing metrics such as temporal versions of betweenness, closeness, k-shell, degree deviation and dynamics-sensitive centralities in one synthetic and five real temporal networks. Experimental results show that the proposed method outperform these well-known methods in identifying critical nodes under spreading dynamic.

Identifying influential spreaders in complex networks by propagation probability dynamics.

Numerous well-known processes of complex systems such as spreading and cascading are mainly affected by a small number of critical nodes. Identifying influential nodes that lead to broad spreading in complex networks is of great theoretical and practical importance. Since the identification of vital nodes is closely related to propagation dynamics, a novel method DynamicRank that employs the probability model to measure the ranking scores of nodes is suggested. The influence of a node can be denoted by the sum of probability scores of its i order neighboring nodes. This simple yet effective method provides a new idea to understand the identification of vital nodes in propagation dynamics. Experimental studies on both Susceptible-Infected-Recovered and Susceptible-Infected-Susceptible models in real networks demonstrate that it outperforms existing methods such as Coreness, H-index, LocalRank, Betweenness, and Spreading Probability in terms of the Kendall τ coefficient. The linear time complexity enables it to be applied to real large-scale networks with tens of thousands of nodes and edges in a short time.

Identifying critical edges in complex networks.

The critical edges in complex networks are extraordinary edges which play more significant role than other edges on the structure and function of networks. The research on identifying critical edges in complex networks has attracted much attention because of its theoretical significance as well as wide range of applications. Considering the topological structure of networks and the ability to disseminate information, an edge ranking algorithm BCCMOD based on cliques and paths in networks is proposed in this report. The effectiveness of the proposed method is evaluated by SIR model, susceptibility index S and the size of giant component σ and compared with well-known existing metrics such as Jaccard coefficient, Bridgeness index, Betweenness centrality and Reachability index in nine real networks. Experimental results show that the proposed method outperforms these well-known methods in identifying critical edges both in network connectivity and spreading dynamic.

Correction: A Novel Top-k Strategy for Influence Maximization in Complex Networks with Community Structure.

[This corrects the article DOI: 10.1371/journal.pone.0145283.].

Identifying a set of influential spreaders in complex networks.

Identifying a set of influential spreaders in complex networks plays a crucial role in effective information spreading. A simple strategy is to choose top-r ranked nodes as spreaders according to influence ranking method such as PageRank, ClusterRank and k-shell decomposition. Besides, some heuristic methods such as hill-climbing, SPIN, degree discount and independent set based are also proposed. However, these approaches suffer from a possibility that some spreaders are so close together that they overlap sphere of influence or time consuming. In this report, we present a simply yet effectively iterative method named VoteRank to identify a set of decentralized spreaders with the best spreading ability. In this approach, all nodes vote in a spreader in each turn, and the voting ability of neighbors of elected spreader will be decreased in subsequent turn. Experimental results on four real networks show that under Susceptible-Infected-Recovered (SIR) and Susceptible-Infected (SI) models, VoteRank outperforms the traditional benchmark methods on both spreading rate and final affected scale. What's more, VoteRank has superior computational efficiency.

A Novel Top-k Strategy for Influence Maximization in Complex Networks with Community Structure.

In complex networks, it is of great theoretical and practical significance to identify a set of critical spreaders which help to control the spreading process. Some classic methods are proposed to identify multiple spreaders. However, they sometimes have limitations for the networks with community structure because many chosen spreaders may be clustered in a community. In this paper, we suggest a novel method to identify multiple spreaders from communities in a balanced way. The network is first divided into a great many super nodes and then k spreaders are selected from these super nodes. Experimental results on real and synthetic networks with community structure show that our method outperforms the classic methods for degree centrality, k-core and ClusterRank in most cases.

Predicting the evolution of spreading on complex networks.

Due to the wide applications, spreading processes on complex networks have been intensively studied. However, one of the most fundamental problems has not yet been well addressed: predicting the evolution of spreading based on a given snapshot of the propagation on networks. With this problem solved, one can accelerate or slow down the spreading in advance if the predicted propagation result is narrower or wider than expected. In this paper, we propose an iterative algorithm to estimate the infection probability of the spreading process and then apply it to a mean-field approach to predict the spreading coverage. The validation of the method is performed in both artificial and real networks. The results show that our method is accurate in both infection probability estimation and spreading coverage prediction.

Evolution characteristics of the network core in the Facebook.

Statistical properties of the static networks have been extensively studied. However, online social networks are evolving dynamically, understanding the evolving characteristics of the core is one of major concerns in online social networks. In this paper, we empirically investigate the evolving characteristics of the Facebook core. Firstly, we separate the Facebook-link(FL) and Facebook-wall(FW) datasets into 28 snapshots in terms of timestamps. By employing the k-core decomposition method to identify the core of each snapshot, we find that the core sizes of the FL and FW networks approximately contain about 672 and 373 nodes regardless of the exponential growth of the network sizes. Secondly, we analyze evolving topological properties of the core, including the k-core value, assortative coefficient, clustering coefficient and the average shortest path length. Empirical results show that nodes in the core are getting more interconnected in the evolving process. Thirdly, we investigate the life span of nodes belonging to the core. More than 50% nodes stay in the core for more than one year, and 19% nodes always stay in the core from the first snapshot. Finally, we analyze the connections between the core and the whole network, and find that nodes belonging to the core prefer to connect nodes with high k-core values, rather than the high degrees ones. This work could provide new insights into the online social network analysis.

Optimizing online social networks for information propagation.

Online users nowadays are facing serious information overload problem. In recent years, recommender systems have been widely studied to help people find relevant information. Adaptive social recommendation is one of these systems in which the connections in the online social networks are optimized for the information propagation so that users can receive interesting news or stories from their leaders. Validation of such adaptive social recommendation methods in the literature assumes uniform distribution of users' activity frequency. In this paper, our empirical analysis shows that the distribution of online users' activity is actually heterogenous. Accordingly, we propose a more realistic multi-agent model in which users' activity frequency are drawn from a power-law distribution. We find that previous social recommendation methods lead to serious delay of information propagation since many users are connected to inactive leaders. To solve this problem, we design a new similarity measure which takes into account users' activity frequencies. With this similarity measure, the average delay is significantly shortened and the recommendation accuracy is largely improved.

Ranking reputation and quality in online rating systems.

How to design an accurate and robust ranking algorithm is a fundamental problem with wide applications in many real systems. It is especially significant in online rating systems due to the existence of some spammers. In the literature, many well-performed iterative ranking methods have been proposed. These methods can effectively recognize the unreliable users and reduce their weight in judging the quality of objects, and finally lead to a more accurate evaluation of the online products. In this paper, we design an iterative ranking method with high performance in both accuracy and robustness. More specifically, a reputation redistribution process is introduced to enhance the influence of highly reputed users and two penalty factors enable the algorithm resistance to malicious behaviors. Validation of our method is performed in both artificial and real user-object bipartite networks.

Identifying influential nodes in large-scale directed networks: the role of clustering.

Identifying influential nodes in very large-scale directed networks is a big challenge relevant to disparate applications, such as accelerating information propagation, controlling rumors and diseases, designing search engines, and understanding hierarchical organization of social and biological networks. Known methods range from node centralities, such as degree, closeness and betweenness, to diffusion-based processes, like PageRank and LeaderRank. Some of these methods already take into account the influences of a node's neighbors but do not directly make use of the interactions among it's neighbors. Local clustering is known to have negative impacts on the information spreading. We further show empirically that it also plays a negative role in generating local connections. Inspired by these facts, we propose a local ranking algorithm named ClusterRank, which takes into account not only the number of neighbors and the neighbors' influences, but also the clustering coefficient. Subject to the susceptible-infected-recovered (SIR) spreading model with constant infectivity, experimental results on two directed networks, a social network extracted from delicious.com and a large-scale short-message communication network, demonstrate that the ClusterRank outperforms some benchmark algorithms such as PageRank and LeaderRank. Furthermore, ClusterRank can also be applied to undirected networks where the superiority of ClusterRank is significant compared with degree centrality and k-core decomposition. In addition, ClusterRank, only making use of local information, is much more efficient than global methods: It takes only 191 seconds for a network with about [Formula: see text] nodes, more than 15 times faster than PageRank.