The determination of the most central agents in complex networks is important because they are responsible for a faster propagation of information, epidemics, failures and congestion, among others. A challenging problem is to identify them in networked systems characterized by different types of interactions, forming interconnected multilayer networks. Here we describe a mathematical framework that allows us to calculate centrality in such networks and rank nodes accordingly, finding the ones that play the most central roles in the cohesion of the whole structure, bridging together different types of relations. These nodes are the most versatile in the multilayer network. We investigate empirical interconnected multilayer networks and show that the approaches based on aggregating-or neglecting-the multilayer structure lead to a wrong identification of the most versatile nodes, overestimating the importance of more marginal agents and demonstrating the power of versatility in predicting their role in diffusive and congestion processes.

Nowadays, millions of people interact on a daily basis on online social media like Facebook and Twitter, where they share and discuss information about a wide variety of topics. In this paper, we focus on a specific online social network, Twitter, and we analyze multiple datasets each one consisting of individuals' online activity before, during and after an exceptional event in terms of volume of the communications registered. We consider important events that occurred in different arenas that range from policy to culture or science. For each dataset, the users' online activities are modeled by a multilayer network in which each layer conveys a different kind of interaction, specifically: retweeting, mentioning and replying. This representation allows us to unveil that these distinct types of interaction produce networks with different statistical properties, in particular concerning the degree distribution and the clustering structure. These results suggests that models of online activity cannot discard the information carried by this multilayer representation of the system, and should account for the different processes generated by the different kinds of interactions. Secondly, our analysis unveils the presence of statistical regularities among the different events, suggesting that the non-trivial topological patterns that we observe may represent universal features of the social dynamics on online social networks during exceptional events.

In online social media networks, individuals often have hundreds or even thousands of connections, which link these users not only to friends, associates, and colleagues, but also to news outlets, celebrities, and organizations. In these complex social networks, a ‘community’ as studied in the social network literature, can have very different meaning depending on the property of the network under study. Taking into account the multifaceted nature of these networks, we claim that community detection in online social networks should also be multifaceted in order to capture all of the different and valuable viewpoints of ‘community.’ In this paper we focus on three types of communities beyond follower-based structural communities: activity-based, topic-based, and interaction-based. We analyze a Twitter dataset using three different weightings of the structural network meant to highlight these three community types, and then infer the communities associated with these weightings. We show that interesting insights can be obtained about the complex community structure present in social networks by studying when and how these four community types give rise to similar as well as completely distinct community structure.

Academic research is driven by several factors causing different disciplines to act as “sources” or “sinks” of knowledge. However, how the flow of authors’ research interests – a proxy of human knowledge – evolved across time is still poorly understood. Here, we build a comprehensive map of such flows across one century, revealing fundamental periods in the raise of interest in areas of human knowledge. We identify and quantify the most attractive topics over time, when a relatively significant number of researchers moved from their original area to another one, causing what we call a “diaspora of the knowledge” towards sinks of scientific interest, and we relate these points to crucial historical and political events. Noticeably, only a few areas – like Medicine, Physics or Chemistry – mainly act as sources of the diaspora, whereas areas like Material Science, Chemical Engineering, Neuroscience, Immunology and Microbiology or Environmental Science behave like sinks.

Probabilistic forecasts play an indispensable role in answering questions about the spread of newly emerged pathogens. However, uncertainties about the epidemiology of emerging pathogens can make it difficult to choose among alternative model structures and assumptions. To assess the potential for uncertainties about emerging pathogens to affect forecasts of their spread, we evaluated the performance 16 forecasting models in the context of the 2015-2016 Zika epidemic in Colombia. Each model featured a different combination of assumptions about human mobility, spatiotemporal variation in transmission potential, and the number of virus introductions. We found that which model assumptions had the most ensemble weight changed through time. We additionally identified a trade-off whereby some individual models outperformed ensemble models early in the epidemic, but on average the ensembles outperformed all individual models. Our results suggest that multiple models spanning uncertainty across alternative assumptions are necessary to obtain robust forecasts for emerging infectious diseases.

haracterizing the socio-economic status of populations and providing reliable and up-to-date estimates of who the most vulnerable are, how many they are, where they live and why they are vulnerable is essential for governments and humanitarian organizations to make informed and timely decisions on implementation of humanitarian assistance policies and programmes 1 . These data are traditionally collected through face-to-face surveys. However, these are expensive, time-consuming and, in certain areas, not possible to perform due to conflict, disease, insecurity or remoteness. Therefore, during the past few years, researchers have begun to investigate the potential of non-traditional data and new computational methods to estimate vulnerabilities and socio-economic characteristics when primary data are not available. In these studies, mobile phone data 2 , satellite imagery 3 , a combination of both 4,5 , mobile money transaction records 6 , geolocated Wikipedia articles 7 or tweets 8 and social media advertising data 9 have been used in combination with state-of-the-art machine learning methods to provide reliable estimates of poverty at different spatial resolutions for several sub-Saharan African countries and southern and southeastern Asian ones.

Nowadays, scientific challenges usually require approaches that cross traditional boundaries between academic disciplines, driving many researchers towards interdisciplinarity. Despite its obvious importance, there is a lack of studies on how to quantify the influence of interdisciplinarity on the research impact, posing uncertainty in a proper evaluation for hiring and funding purposes. Here we propose a method based on the analysis of bipartite interconnected multilayer networks of citations and disciplines, to assess scholars, institutions and countries interdisciplinary importance. Using data about physics publications and US patents, we show that our method allows to reward, using a quantitative approach, scholars and institutions that have carried out interdisciplinary work and have had an impact in different scientific areas. The proposed method could be used by funding agencies, universities and scientific policy decision makers for hiring and funding purposes, and to complement existing methods to rank universities and countries.

The chapter “Multilayer Networks” introduces the topic of interconnected multilayer networks, analyzing them from a few fronts: types of multilayer networks, their mathematical description, the dynamics of random walks, and the centrality (versatility) of nodes. Multilayer networks appear naturally in real data as, in many cases, the relationships (links) between the elements (nodes) can be of different kinds. For example, people can be connected through friendship, family relations, or work relations. This structure can be represented as a network formed by three layers, one for each type of relationship, with the same nodes repeated in all layers. Thus, there are different behaviors in each layer, and interactions between them, which result in more realistic but, at the same time, more complex dynamics. This chapter shows how interconnected multilayer topology describes such networks more accurately than edge coloring does and introduces the tensor formalism used to construct them.