[June 2017 update] This tutorial is continuously updated and expanded. The latest version includes additional information (more on multiplex graphs, interactive JS networks, geographic data, etc). If you want to see earlier versions, they are still available here: 2015 and 2016. You can also get the new tutorial PDF and code here or on GithHub.
If you find the tutorial useful, please cite it in your work – this helps me make the case that open publishing of digital materials like this is a meaningful academic contribution: Ognyanova, K. (2017) Network visualization with R. Retrieved from www.kateto.net/network-visualization.