Acting as a complete amateur (two weeks in), below is a quick attempt at implementing a few of these concepts on a familiar network: a RISK game board. RISK is a game that simulates Earth's countries (some are regions) with the objective of dominating the globe by winning battles with other players. One can be attacked only by an adjacent country, so it quickly becomes clear that some countries are harder to defend than others. For example, Afghanistan touches six countries while Peru touches only two. Below is the game map:
At right is a chart summarizing the number of adjacent countries. Note that this link is often called an "edge." Basically, there are a few countries conducive to isolationist-style players (holing up in Australia is a common strategy for meek players who want to inherit the Earth). Countries exposed to five or six other countries can be difficult to defend. However, as a player's realm expands the only edges of concern are the outermost ones; internal boundaries can only be reached if the perimeter is first breached.
The course uses network analysis software called Pajek. I loaded in the RISK countries (vertices) and their neighbors (edges are technically the link between), then let the software draw a reasonable approximation of the true map that I tweaked manually. Of special note, is the Alaska-Kamchatka connection that the board game displays as wrapping around the back of the globe.