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This series of blog posts provides an extremely accessible and clear introduction to networks and graph theory. They are written by someone with a strong background in digital humanities. Start with the first post, and then check out the other 8 (or so posts) in the series here and here.
Topic Modeling
Each of the articles below provides an introduction to topic models from a somewhat different perspective and for a somewhat different audience. Don't feel obliged to read all of them in detail. Instead, take a brief look at each, and try to find one or two that seem especially accessible to you. Some will prefer a more technical explanation, others may find a more abstract explanation to be preferable.