Socilyzer is described as 'An all-in-one organizational and social network analysis tool used by managers and management consultants'. There are eight alternatives to Socilyzer, not only websites but also apps for a variety of platforms, including Windows, Linux, Mac and iPad. The best alternative is Gephi, which is both free and Open Source. Other great sites and apps similar to Socilyzer are Cytoscape (Free, Open Source), Polinode (Paid), KeyLines Graph Visualization Toolkit (Paid) and NodeXL (Free, Open Source).
Cytoscape is an open source software platform for visualizing complex networks and integrating these with any type of attribute data. A lot of plugins are available for various kinds of problem domains, including bioinformatics, social network analysis, and semantic web.
Polinode is a tool that makes it easy to perform powerful network analysis. You can either upload your own network data or use the integrated relationship-based survey tool to collect data for you before analyzing and visualizing your networks.