A measure of centrality is rank monotone if after adding an arc x → y, all nodes with a score smaller than (or equal to) y have still a score smaller than (or equal to) y. If, in particular, all nodes with a score smaller than or equal to y get a score smaller than y (i.e., all ties with y are broken in favor of y), the measure is called strictly rank monotone. We prove that harmonic centrality is strictly rank monotone, whereas closeness is just rank monotone on strongly connected graphs, and that some other measures, including betweenness, are not rank monotone at all (sometimes not even on strongly connected graphs). Among spectral measures, damped scores such as Katz's index and PageRank are strictly rank monotone on all graphs, whereas the dominant eigenvector is strictly monotone on strongly connected graphs only.

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.

We study the incentives that agents have to invest in costly protection against cascading failures in networked systems. Applications include vaccination, computer security, and airport security. Agents are connected through a network and can fail either intrinsically or as a result of the failure of a subset of their neighbors. We characterize the equilibrium based on an agent's failure probability and derive conditions under which equilibrium strategies are monotone in degree (i.e. in how connected an agent is on the network). We show that different kinds of applications (e.g. vaccination, malware, airport/EU security) lead to very different equilibrium patterns of investments in protection, with important welfare and risk implications. Our equilibrium concept is flexible enough to allow for comparative statics in terms of network properties, and we show that it is also robust to the introduction of global externalities (e.g. price feedback, congestion).

Research in the area of social networks and health has demonstrated that lay social network members play a critical role in the early stages of the illness career, influencing key decisions and pathways to formal care. Here, we revisit and extend this body of work, examining how the lay social network context can moderate the influence of treatment experiences on recovery outcomes as the illness career unfolds. To achieve this goal, we address two research questions, drawing on a longitudinal sample of people making their initial contact with the mental health treatment system: First, we explore how treatment experiences, lay social network characteristics, and recovery outcomes change over 2 years, beginning with the point of entry into treatment. Second, we examine whether the relationship between perceived treatment experiences and recovery outcomes is contingent on characteristics of the lay network context in which clients are socially embedded, focusing on the network's cultural orientation toward medical professionals. We find that positive treatment interactions facilitate improved self-esteem, mastery, role functioning, recovery optimism, and global functioning when the lay network culture is pro-medical, but largely have null effects on the recovery process when the lay network is more hostile to medical professionals.

Critical to the development of improved HIV elimination efforts is a greater understanding of how social networks and their dynamics are related to HIV risk and prevention. In this paper, we examine network stability of confidant and sexual networks among young black men who have sex with men (YBMSM). We use data from uConnect (2013–2016), a population-based, longitudinal cohort study. We use an innovative approach to measure both sexual and confidant network stability at three time points, and examine the relationship between each type of stability and HIV risk and prevention behaviors. This approach is consistent with a co-evolutionary perspective in which behavior is not only affected by static properties of an individual's network, but may also be associated with changes in the topology of his or her egocentric network. Our results indicate that although confidant and sexual network stability are moderately correlated, their dynamics are distinct with different predictors and differing associations with behavior. Both types of stability are associated with lower rates of risk behaviors, and both are reduced among those who have spent time in jail. Public health awareness and engagement with both types of networks may provide new opportunities for HIV prevention interventions.

The order of the authors in the published article is incorrect. The authors should appear as follows:

J. Schneider, B. Cornwell, A. Jonas, R. Behler, N. Lancki, B. Skaathun, L. E. Young, E. Morgan, S. Michaels, R. Duvoisin, A. S. Khanna, S. Friedman, P. Schumm, E. Laumann, for the uConnect Study Team

The authors regret the error.