Network analysis can simply be understood as the analysis of social networks. The analysis provides a visual representation of different members (or nodes) within a network, and how they connect to each other.
I use Gephi to visualize networks based on data from Twitter and Facebook. I would highly recommend the following book: Analyzing the Social Web by Jennifer Golbeck (available on Amazon), to understand social network analysis.
Here are a few videos that are useful in understanding social network analysis using Gephi.
Video 1: Visual Analysis of Social Networks
Video 2: A Walkthrough Analysis of Tor Networks in Gephi
Video 3: Gephi Tutorial: Finding Shortest Paths
Video 4: Gephi Labels and Colors
Video 5: Gephi Modularity Tutorial
Video 6: Gephi Tutorial: Filtering Networks
Video 7: How to Look at Node Labels in Gephi
Video 8: Gephi Tutorial on Network Visualization and Analysis