VOSviewer. A software tool made for "constructing and visualizing bibliometric networks. These networks may, for instance, include journals, researchers, or individual publications, and they can be constructed based on citation, bibliographic coupling, co-citation, or co-authorship relationships." Free to download and use.
CiteSpace. A Java-supported tool for "visualizing and analyzing trends and patterns in scientific literature. Primarily used for Web of Science, though data from other sides such as arXiv, PubMed, and NSF Award Abstracts can be obtained. Free to download and use.
Bibliometrix. An open-source R-tool that is used to complete complex scientific bibliometric analysis. It uses data from Scopus, Web of Science, Dimensions, PubMed, and Cochrane. A version called biblioshiny has been released for use in R for non-coders. Free to download and use..
Gephi. An open-source network and visualization software that allows users to import data from almost anywhere under-supported file formats. Requires knowledge of Java and/or OpenGL to use fully. Free to use and download.
Sci2. A scientific visualization and analysis tool that scientists and librarians designed for scientists. Free to download and use.