R is a powerful open source statistical computing application. It has easy scripting, visual output, and data analysis. Network analysis is easy with the igraph package (see below).
Agna is another Java based tool with a nice interface for data entry/editing, and a separate window for visualization and layout.
Gephi an open-source, cross platform tool for network exploration. Makes beautiful, highly customizable, plots.
GUESS is a powerful visualization and analysis tool written with Python.
Tulip is open source and written with Qt/C++/OpenGL and has a lot of interesting, interactive features, not to mention a beautiful logo. The interface is very creative, and documentation is extensive.
SocNetV is an open-source graph manipulation/visualiation appliation for Linux, built with C++ and Qt (Qt4 package required) with a simple graphical interface. Easy to use, keeps it simple.
SoNIA is a Social Network Image Animator, and can be used to create interesting layouts, as well as videos of evolving networks.
NetworkX is an open-source, terminal-based python program with simple commands and lots of features for manipulation and visualization of graphs.
Network Workbench is a powerful application written in Java with lots of analysis tools, though the interface is not very friendly.
Pajek (old) is a popular layout and analysis tool that has a lot of good features. It is, however, only for Windows, and is not open source.
FANMOD is “a tool for fast network motif detection”, multi-platform binaries and source code are available. Has GUI and command-line versions.
NAViGaTOR is written in JAVA with OpenGL for visualization and analysis of biological networks.
NetVis is a web-based and open-source tool for network data collection, visualization, and analysis. It is written in PHP and Java.
yED is a Java-based graph drawing and layout tool with some data anlaysis. Drawings and layout for graphs and diagrams are interactive, and look nice.
Programming libraries
igraph is a great package for graph manipulation, generation and visualization. Library is written in ANSI C, and works with C/C++, R, Python, and Ruby.
Boost Graph Library is a powerful library class with lots of flexibility in data structures, and includes pretty much any algorithm you might need.
Open Graph Drawing Framework is an easy to use, self-contained class library for analysis and layout, written in C++.
JUNG is a Java-based class library for graph visualization.
Academic journals, research groups, societies
International Network for Social Network Analysis
Social Networks
Journal of Social Structure
REDES: Revista Hispana para el análisis de Redes Sociales
Physical Review E
Journal of Mathematical Sociology
Learning resources
Graph Theory, a free textbook by Reinhard Diestel. Full online version available in English and German.
Free textbooks including: Introduction to social network methods and Computer-Assisted Theory Building: Modeling Dynamic Social Systems by Robert Hanneman, and others.
Dynamics of Complex Systems, a free textbook by Yaneer Bar-Yam.
Graph theory glossary is a good Wikipedia list of annoted graph theory terminology
Data Sets
Gephi Data Sets Les Miserables, Zachary’s Karate Club, Github open-source developers, and others in a variety of formats.
MEJ Newman’s Page College football, dolphins, power grid, collaborations in network science, all GML format
NetWiki Shared Data Brain, Facebook, MLB hitter-batter matchups, variety of formats
Fun
Muckety is a news source that investigates the people and connections behind the headlines, and has interactive social network maps of the rich and powerful.