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Religious beliefs could facilitate human cooperation [1-6], promote civic engagement [7-10], improve life satisfaction [11-13] and even boom economic development [14-16]. On the other side, some aspects of religion may lead to regional violence, intergroup conflict and moral prejudice against atheists [17-23]. Analogous to the separation of races [24], the religious segregation is a major ingredient resulting in increasing alienation, misunderstanding, cultural conflict and even violence among believers of different faiths [18,19,25]. Thus far, quantitative understanding of religious segregation is rare. Here we analyze a directed social network extracted from weibo.com (the largest directed social network in China, similar to twitter.com), which is consisted of 6875 believers in Christianism, Buddhism, Islam and Taoism. This religion network is highly segregative, with only 1.6% of links connecting individuals in different religions. Comparative analysis shows that the extent of segregation for different religions is much higher than that for different races and slightly higher than that for different political parties. The few cross-religion links play a critical role in maintaining network connectivity, being remarkably more important than links with highest betweennesses [26] or bridgenesses [27]. Further content analysis shows that 46.7% of these cross-religion links are probably related to charitable issues. Our findings provide quantitative insights into religious segregation and valuable clues to encourage cross-religion communications., Comment: 11 pages, 2 figures

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., Comment: 121Pages, 20 figures

Enterprises have put more and more emphasis on data analysis so as to obtain effective management advices. Managers and researchers are trying to dig out the major factors that lead to employees' promotion and resignation. Most previous analyses were based on questionnaire survey, which usually consists of a small fraction of samples and contains biases caused by psychological defense. In this paper, we successfully collect a data set consisting of all the employees' work-related interactions (action network, AN for short) and online social connections (social network, SN for short) of a company, which inspires us to reveal the correlations between structural features and employees' career development, namely promotion and resignation. Through statistical analysis and prediction, we show that the structural features of both AN and SN are correlated and predictive to employees' promotion and resignation, and the AN has higher correlation and predictability. More specifically, the in-degree in AN is the most relevant indicator for promotion; while the k-shell index in AN and in-degree in SN are both very predictive to resignation. Our results provide a novel and actionable understanding of enterprise management and suggest that to enhance the interplays among employees, no matter work-related or social interplays, can largely improve the loyalty of employees., Comment: 8 pages, 3 figures and 1 table

Numerous concise models such as preferential attachment have been put forward to reveal the evolution mechanisms of real-world networks, which show that real-world networks are usually jointly driven by a hybrid mechanism of multiplex features instead of a single pure mechanism. To get an accurate simulation for real networks, some researchers proposed a few hybrid models of mixing multiple evolution mechanisms. Nevertheless, how a hybrid mechanism of multiplex features jointly influence the network evolution is not very clear. In this study, we introduce two methods (link prediction and likelihood analysis) to measure multiple evolution mechanisms of complex networks. Through tremendous experiments on artificial networks, which can be controlled to follow multiple mechanisms with different weights, we find the method based on likelihood analysis performs much better and gives very accurate estimations. At last, we apply this method to some real-world networks which are from different domains (including technology networks and social networks) and different countries (e.g., USA and China), to see how popularity and clustering co-evolve. We find most of them are affected by both popularity and clustering, but with quite different weights., Comment: 21 pages, 5 figures

Homophily is a significant mechanism for link prediction in complex network, of which principle describes that people with similar profiles or experiences tend to tie with each other. In a multi-relationship network, friendship among people has been utilized to reinforce similarity of taste for recommendation system whose basic idea is similar to homophily, yet how the taste inversely affects friendship prediction is little discussed. This paper contributes to address the issue by analyzing two benchmark datasets both including user's behavioral information of taste and friendship based on the principle of homophily. It can be found that the creation of friendship tightly associates with personal taste. Especially, the behavioral information of taste involving with popular objects is much more effective to improve the performance of friendship prediction. However, this result seems to be contradictory to the finding in [Q.M. Zhang, et al., PLoS ONE 8(2013)e62624] that the behavior information of taste involving with popular objects is redundant in recommendation system. We thus discuss this inconformity to comprehensively understand the correlation between them., Comment: 8 pages, 5 figures

Link prediction aims to uncover missing links or predict the emergence of future relationships according to the current networks structure. Plenty of algorithms have been developed for link prediction in unweighted networks, with only a very few of them having been extended to weighted networks. Thus far, how to predict weights of links is important but rarely studied. In this Letter, we present a reliable-route-based method to extend unweighted local similarity indices to weighted indices and propose a method to predict both the link existence and link weights accordingly. Experiments on different real networks suggest that the weighted resource allocation index has the best performance to predict the existence of links, while the reliable-route-based weighted resource allocation index performs noticeably better on weight prediction. Further analysis shows a strong correlation for both link prediction and weight prediction: the larger the clustering coefficient, the higher the prediction accuracy., Comment: 5 pages, 4 tables

Food occupies a central position in every culture and it is therefore of great interest to understand the evolution of food culture. The advent of the World Wide Web and online recipe repositories has begun to provide unprecedented opportunities for data-driven, quantitative study of food culture. Here we harness an online database documenting recipes from various Chinese regional cuisines and investigate the similarity of regional cuisines in terms of geography and climate. We found that the geographical proximity, rather than climate proximity is a crucial factor that determines the similarity of regional cuisines. We develop a model of regional cuisine evolution that provides helpful clues to understand the evolution of cuisines and cultures., Comment: 13 pages, 11 figures and 2 tables

Information overload is a serious problem in modern society and many solutions such as recommender system have been proposed to filter out irrelevant information. In the literature, researchers mainly dedicated to improve the recommendation performance (accuracy and diversity) of the algorithms while overlooked the influence of topology of the online user-object bipartite networks. In this paper, we find that some information provided by the bipartite networks is not only redundant but also misleading. With such "less can be more" feature, we design some algorithms to improve the recommendation performance by eliminating some links from the original networks. Moreover, we propose a hybrid method combining the time-aware and topology-aware link removal algorithms to extract the backbone which contains the essential information for the recommender systems. From the practical point of view, our method can improve the performance and reduce the computational time of the recommendation system, thus improve both of their effectiveness and efficiency.

Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation., Comment: 8 pages, 6 figures

Many models are put forward to mimic the evolution of real networked systems. A well-accepted way to judge the validity is to compare the modeling results with real networks subject to several structural features. Even for a specific real network, we cannot fairly evaluate the goodness of different models since there are too many structural features while there is no criterion to select and assign weights on them. Motivated by the studies on link prediction algorithms, we propose a unified method to evaluate the network models via the comparison of the likelihoods of the currently observed network driven by different models, with an assumption that the higher the likelihood is, the better the model is. We test our method on the real Internet at the Autonomous System (AS) level, and the results suggest that the Generalized Linear Preferential (GLP) model outperforms the Tel Aviv Network Generator (Tang), while both two models are better than the Barab\'asi-Albert (BA) and Erd\"os-R\'enyi (ER) models. Our method can be further applied in determining the optimal values of parameters that correspond to the maximal likelihood. Experiment indicates that the parameters obtained by our method can better capture the characters of newly-added nodes and links in the AS-level Internet than the original methods in the literature., Comment: 6 pages, 2 figures, 3 tables

Common-neighbor-based method is simple yet effective to predict missing links, which assume that two nodes are more likely to be connected if they have more common neighbors. In such method, each common neighbor of two nodes contributes equally to the connection likelihood. In this Letter, we argue that different common neighbors may play different roles and thus lead to different contributions, and propose a local na\"{\i}ve Bayes model accordingly. Extensive experiments were carried out on eight real networks. Compared with the common-neighbor-based methods, the present method can provide more accurate predictions. Finally, we gave a detailed case study on the US air transportation network., Comment: 6 pages, 2 figures, 2 tables

To evaluate the performance of prediction of missing links, the known data are randomly divided into two parts, the training set and the probe set. We argue that this straightforward and standard method may lead to terrible bias, since in real biological and information networks, missing links are more likely to be links connecting low-degree nodes. We therefore study how to uncover missing links with low-degree nodes, namely links in the probe set are of lower degree products than a random sampling. Experimental analysis on ten local similarity indices and four disparate real networks reveals a surprising result that the Leicht-Holme-Newman index [E. A. Leicht, P. Holme, and M. E. J. Newman, Phys. Rev. E 73, 026120 (2006)] performs the best, although it was known to be one of the worst indices if the probe set is a random sampling of all links. We further propose an parameter-dependent index, which considerably improves the prediction accuracy. Finally, we show the relevance of the proposed index on three real sampling methods., Comment: 16 pages, 5 figures, 6 tables

We propose a similarity-based method, using the similarity between nodes, to address the problem of classification in partially labeled networks. The basic assumption 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 classification 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 sparce the global indices perform better. Besides, the similarity-based method can to some extent overcome the unconsistency problem which is another difficulty in classification., Comment: 13 pages,3 figures,1 table