At its most basic level, a network is any connection to anything else. In order for a network to be meaningful, it has to be a system of elements or entities that are connected by relationships. These relationships are the defining feature of networks, as opposed to content or components. People study networks because they believe that the network itself is in some way significant and that the parts that make up the network are interdependent, not independent. Network analysis can be used to identify emerging patterns within a dataset. One kind of network analysis is social network analysis, which analyzes social structures through the use of networks.
Palladio is a project of Stanford's Humanities + Design Research Lab. The web-based application is free to use. You are able to import your tabular data into Palladio and visualize it in a map, graph, table, or gallery view. You can change the size of the dots (nodes) for each visualization to correlate with the frequency with which they appear in your dataset. Your Palladio project is exportable and you can revisit it at a later time within the platform.
Project using Palladio: Andrew W. Wilson, Mapping the Revolution (2016)
Gephi is a free and open source visualization software for graphs and networks. Gephi can be used for exploratory data, link, social network, and biological network analyses. Users can create real-time visualizations with networks of up to 100,000 nodes and 1,000,000 edges. You can add to the functionality of the software by installing plugins. Gephi is notoriously buggy and has not been updated in several years but is still useful software for network analysis.
Project using Gephi: Gönül Aycı, A Simple Project With Gephi (2017)
The following tools can be utilized to analyze citations. These tools create networks from the analyzed data and many also include commonly used metrics.
The following tools are free to use. See KDNuggets' Top 30 Social Network Analysis & Visualization Tools for a comprehensive review of major social network analysis and visualization tools.