This response is for part I, so apologies if anything I mention is covered in the second part. I agree with the other posts that this is generally a well written and easily readable introduction to networks. As the first part of an introductory article, I’ll try to focus my comments on the ease of understanding the material that you’re presenting.
The most confusing aspect, to me, was the immediate jump into complex graph types in “The Stuff”. As you yourself pointed out, bi- and multi- partite graphs are more complicated and less rigorously studied. A little more time illustrating the most basic graphs, and how they help model data, would help your readers understand the power that networks offer in the kinds of analysis you discuss. As examples you could use something like a graph of citations (directed) or a graph of distances between cities (undirected). Showing how you could analytically determine the “influence” of a paper, or the “difficulty” in moving between two cities, would then naturally move to showing how each of those has central nodes (most influential paper, city closest to the center). When you bring up node centrality in bi-partite graphs, your readers would then have a basis for understanding why that calculation is not meaningful. The same ideas holds true for your section on “The Relationships”. Once you have helped your readers understand graphs with a single type of node and single type of edge, you could move into more complicated graph types.
The second are in which I would suggest more development is when graphs are appropriate, and when they aren’t. You mention in your “Some Warnings” section that it is easy to over-apply network analysis to problems. Your books and authors relationship could be a cautionary example in itself, I was not clear what analytical information you wanted, or would be able to get, out of that example. The tables that you presented with Author and Book data would appear to be perfect candidates for a structured database. It has clearly defined fields, obvious “key” fields, and multiple ways to relate tables to each other. Going into more detail as to why you chose a network to represent this data would go a long way towards helping your audience understand the how and why of network analysis.
With the criticism out of the way, I am looking forward to reading part II, and any other future parts you have.
