Significance: The wide availability of user-provided content in online social media facilitates the aggregation of people around common interests, worldviews, and narratives. However, the World Wide Web is a fruitful environment for the massive diffusion of unverified rumors. In this work, using a massive quantitative analysis of Facebook, we show that information related to distinct narratives––conspiracy theories and scientific news––generates homogeneous and polarized communities (i.e., echo chambers) having similar information consumption patterns. Then, we derive a data-driven percolation model of rumor spreading that demonstrates that homogeneity and polarization are the main determinants for predicting cascades’ size.

Systemic risk, here meant as the risk of default of a large portion of the financial system, depends on the network of financial exposures among institutions. However, there is no widely accepted methodology to determine the systemically important nodes in a network. To fill this gap, we introduce, DebtRank, a novel measure of systemic impact inspired by feedback-centrality. As an application, we analyse a new and unique dataset on the USD 1.2 trillion FED emergency loans program to global financial institutions during 2008–2010. We find that a group of 22 institutions, which received most of the funds, form a strongly connected graph where each of the nodes becomes systemically important at the peak of the crisis. Moreover, a systemic default could have been triggered even by small dispersed shocks. The results suggest that the debate on too-big-to-fail institutions should include the even more serious issue of too-central-to-fail.

A new mechanism leading to scale-free networks is proposed in this Letter. It is shown that, in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Assigning a quenched fitness value $x_i$ to every vertex, and drawing links among vertices with a probability depending on the fitnesses of the two involved sites, gives rise to what we call a good-get-richer mechanism, in which sites with larger fitness are more likely to become hubs (i.e., to be highly connected).

A variety of different social, natural and technological systems can be described by the same mathematical framework. This holds from the Internet to food webs and to boards of company directors. In all these situations, a graph of the elements of the system and their interconnections displays a universal feature. There are only a few elements with many connections and many elements with few connections. This book reports the experimental evidence of these ‘Scale-free networks’ and provides students and researchers with a corpus of theoretical results and algorithms to analyse and understand these features. The content of this book and the exposition makes it a clear textbook for beginners and a reference book for experts.

Classical economic theories prescribe specialization of countries industrial production. Inspection of the country databases of exported products shows that this is not the case: successful countries are extremely diversified, in analogy with biosystems evolving in a competitive dynamical environment. The challenge is assessing quantitatively the non-monetary competitive advantage of diversification which represents the hidden potential for development and growth. Here we develop a new statistical approach based on coupled non-linear maps, whose fixed point defines a new metrics for the country Fitness and product Complexity. We show that a non-linear iteration is necessary to bound the complexity of products by the fitness of the less competitive countries exporting them. We show that, given the paradigm of economic complexity, the correct and simplest approach to measure the competitiveness of countries is the one presented in this work. Furthermore our metrics appears to be economically well-grounded.

The large availability of user provided contents on online social media facilitates people aggregation around shared beliefs, interests, worldviews and narratives. In spite of the enthusiastic rhetoric about the so called collective intelligence unsubstantiated rumors and conspiracy theories—e.g., chemtrails, reptilians or the Illuminati—are pervasive in online social networks (OSN). In this work we study, on a sample of 1.2 million of individuals, how information related to very distinct narratives—i.e. main stream scientific and conspiracy news—are consumed and shape communities on Facebook. Our results show that polarized communities emerge around distinct types of contents and usual consumers of conspiracy news result to be more focused and self-contained on their specific contents. To test potential biases induced by the continued exposure to unsubstantiated rumors on users’ content selection, we conclude our analysis measuring how users respond to 4,709 troll information—i.e. parodistic and sarcastic imitation of conspiracy theories. We find that 77.92% of likes and 80.86% of comments are from users usually interacting with conspiracy stories.