The number of papers published in journals indexed by the Web of Science core collection is steadily increasing. In recent years, nearly two million new papers were published each year; somewhat more than one million papers when primary research papers are considered only (articles and reviews are the document types where primary research is usually reported or reviewed). However, who reads these papers? More precisely, which groups of researchers from which (self-assigned) scientific disciplines and countries are reading these papers? Is it possible to visualize readership patterns for certain countries, scientific disciplines, or academic status groups? One popular method to answer these questions is a network analysis. In this study, we analyze Mendeley readership data of a set of 1,133,224 articles and 64,960 reviews with publication year 2012 to generate three different kinds of networks: (1) The network based on disciplinary affiliations of Mendeley readers contains four groups: (i) biology, (ii) social science and humanities (including relevant computer science), (iii) bio-medical sciences, and (iv) natural science and engineering. In all four groups, the category with the addition "miscellaneous" prevails. (2) The network of co-readers in terms of professional status shows that a common interest in papers is mainly shared among PhD students, Master's students, and postdocs. (3) The country network focusses on global readership patterns: a group of 53 nations is identified as core to the scientific enterprise, including Russia and China as well as two thirds of the OECD (Organisation for Economic Co-operation and Development) countries.