Besides its really impressive and useful data visualization, the igraph package has a lot more to offer. Unfortunately, this short chapter cannot provide a decent introduction to network analysis theory, but I suggest that you skim through the package documentation as it comes with useful, self-explanatory examples and good references.
In short, network analysis provides various ways to compute centrality and density metrics, like we did at the beginning of this chapter, and also to identify bridges and simulate changes in the network; there are really powerful methods to segment the nodes in the network as well.
For example, in the Financial Networks chapter of the Introduction to R for Quantitative Finance book, which I coauthored, we developed R scripts to identify systemically important financial institutions(SIFI) in Hungary based on the transaction-level network data of the interbank lending market. This dataset and network theory help us to model and potentially predict future financial crises, and also to simulate the effect of central intervention.
A more detailed, freely available summary on this research was presented at the R/Finance 2015 conference in Chicago http://www.rinfinance.com/agenda/2015/talk/GergelyDaroczi.pdf, along with a Shiny application https://bit.ly/rfin2015-hunbanks, and a related, simulation-based infection-model was described in the Systemic Risk chapter of the Mastering R for Quantitative Finance book as well.
The main idea behind this joint research was to identify core, peripheral, and semi-peripheral financial institutions based on the network formed by interbank lending transactions. The nodes being banks, the edges are defined as lend events between those, so we can interpret the bridges between periphery nodes as the intermediary bank between smaller banks, which usually do not lend money to each other directly.
The interesting question, after resolving some technical issues with the dataset, was to simulate what happens if an intermediary bank defaults, and if this unfortunate event might also affect other financial institutions.