Gephi  

https://gephi.org

Gephi is an open-source tool for network visualisation and analysis. It provides features to visually manipulate a network. 

Citation: Bastian M., Heymann S., Jacomy M. (2009). Gephi: an open-source software for exploring and manipulating networks. International AAAI Conference on Weblogs and Social Media. 

NetworkX/Python 

https://networkx.org/documentation/stable/index.html

NetworkX is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks. 

Citation: Aric A. Hagberg, Daniel A. Schult and Pieter J. Swart, “Exploring network structure, dynamics, and function using NetworkX”, in Proceedings of the 7th Python in Science Conference (SciPy2008), Gäel Varoquaux, Travis Vaught, and Jarrod Millman (Eds), (Pasadena, CA USA), pp. 11–15, Aug 2008 

NodeXL 

https://www.smrfoundation.org/nodexl/

NodeXL Basic (free version) is an add-in for Microsoft Excel that supports social network and content analysis.   

Citation: Smith, M., Ceni A., Milic-Frayling, N., Shneiderman, B., Mendes Rodrigues, E., Leskovec, J., Dunne, C., (2010). NodeXL: a free and open network overview, discovery and exploration add-in for Excel 2007/2010/2013/2016, from the Social Media Research Foundation.

R/igraph 

https://igraph.org

igraph is an open-source package which integrates network analysis tools (network metrics and visualisation). igraph can be programmed in Pyhton, Mathematica and C/C++. 
 
Manual pages: https://igraph.org/r/doc/ 

Citation: Csardi G, Nepusz T (2006). “The igraph software package for complex network research.” InterJournal, Complex Systems, 1695.

R/vosonSML and R/VOSONDash

vosonSML (available on CRAN and GitHub) is an R package for the collection of social media data (Twitter, YouTube and Reddit) and the creation of various social networks for analysis. VOSON Dashboard (available on CRAN and GitHub) is an interactive R shiny app that integrates social media data collection (via vosonSML),  network visualisation and analysis tools. 

vosonSML and VOSONDash are developed at the VOSON Lab, School of Sociology, ANU.

vosonSML GitHub page: https://github.com/vosonlab/vosonSML 
vosonSML vignette : https://vosonlab.github.io/vosonSML/articles/Intro-to-vosonSML.html 

VOSON Dashboard GitHub page: https://github.com/vosonlab/VOSONDash 
VOSON Dashboard userguide: https://vosonlab.github.io/VOSONDashDocs/

R/statnet

http://statnet.org/

statnet is a suite of R packages for the management, exploration, statistical analysis, simulation and vizualization of network data.

Citation: Statnet Development Team, (Pavel N. Krivitsky, Mark S. Handcock, David R. Hunter, Carter T. Butts, Chad Klumb, Steven M. Goodreau, and Martina Morris) (2003-2020).
statnet: Software tools for the Statistical Modeling of Network Data.