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Register a new userA Superintroduction to Google Matrices for Undergraduates
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In this paper we consider so-called Google matrices and show that all eigenvalues ($lambda$) of them have a fundamental property $|lambda|leq 1$. The stochastic eigenvector corresponding to $lambda=1$ called the PageRank vector plays a central role in the Googles software. We study it in detail and present some important problems. The purpose of the paper is to make {bf the heart of Google} clearer for undergraduates.
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We construct the Google matrix of the entire Twitter network, dated by July 2009, and analyze its spectrum and eigenstate properties including the PageRank and CheiRank vectors and 2DRanking of all nodes. Our studies show much stronger inter-connectivity between top PageRank nodes for the Twitter network compared to the networks of Wikipedia and British Universities studied previously. Our analysis allows to locate the top Twitter users which control the information flow on the network. We argue that this small fraction of the whole number of users, which can be viewed as the social network elite, plays the dominant role in the process of opinion formation on the network.
A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local richness of the cyclic structure. In this paper, we introduce renewal non-backtracking random walks (RNBRW) as a way of quantifying this structure. RNBRW gives a weight to each edge equal to the probability that a non-backtracking random walk completes a cycle with that edge. Hence, edges with larger weights may be thought of as more important to the formation of cycles. Of note, since separate random walks can be performed in parallel, RNBRW weights can be estimated very quickly, even for large graphs. We give simulation results showing that pre-weighting edges through RNBRW may substantially improve the performance of common community detection algorithms. Our results suggest that RNBRW is especially efficient for the challenging case of detecting communities in sparse graphs.
Segregation is the separation of social groups in the physical or in the online world. Segregation discovery consists of finding contexts of segregation. In the modern digital society, discovering segregation is challenging, due to the large amount and the variety of social data. We present a tool in support of segregation discovery from relational and graph data. The SCube system builds on attributed graph clustering and frequent itemset mining. It offers to the analyst a multi-dimensional segregation data cube for exploratory data analysis. The demonstration first guides the audience through the relevant social science concepts. Then, it focuses on scenarios around case studies of gender occupational segregation. Two real and large datasets about the boards of directors of Italian and Estonian companies will be explored in search of segregation contexts. The architecture of the SCube system and its computational efficiency challenges and solutions are discussed.
Massive amounts of misinformation have been observed to spread in uncontrolled fashion across social media. Examples include rumors, hoaxes, fake news, and conspiracy theories. At the same time, several journalistic organizations devote significant efforts to high-quality fact checking of online claims. The resulting information cascades contain instances of both accurate and inaccurate information, unfold over multiple time scales, and often reach audiences of considerable size. All these factors pose challenges for the study of the social dynamics of online news sharing. Here we introduce Hoaxy, a platform for the collection, detection, and analysis of online misinformation and its related fact-checking efforts. We discuss the design of the platform and present a preliminary analysis of a sample of public tweets containing both fake news and fact checking. We find that, in the aggregate, the sharing of fact-checking content typically lags that of misinformation by 10--20 hours. Moreover, fake news are dominated by very active users, while fact checking is a more grass-roots activity. With the increasing risks connected to massive online misinformation, social news observatories have the potential to help researchers, journalists, and the general public understand the dynamics of real and fake news sharing.
Measuring the geographical distribution of economic activity plays a key role in scientific research and policymaking. However, previous studies and data on economic activity either have a coarse spatial resolution or cover a limited time span, and the high-resolution characteristics of socioeconomic dynamics are largely unknown. Here, we construct a dataset on the economic activity of mainland China, the gridded establishment dataset (GED), which measures the volume of establishments at a 0.01$^{circ}$ latitude by 0.01$^{circ}$ longitude scale. Specifically, our dataset captures the geographically based opening and closing of approximately 25.5 million firms that registered in mainland China over the period 2005-2015. The characteristics of fine granularity and long-term observability give the GED a high application value. The dataset not only allows us to quantify the spatiotemporal patterns of the establishments, urban vibrancy and socioeconomic activity, but also helps us uncover the fundamental principles underlying the dynamics of industrial and economic development.
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