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I'm writing my master thesis in network formation theory. I believe that a picture with network nodes in the introduction will help the readers understand what my model is and what I am trying to prove. I doubt most readers would read past the introduction anyway so if they do not understand the introduction then that would be a big problem for me.
Is that advisable or not? What if I am using the introduction as the writing sample for my PhD application?
I can't think of any reason in general that you should not do this if it makes sense in the context of the paper. If you can express the underlying concept better with a figure then it is better than to use words.
But an advisor might disagree, in the context of this paper. And an editor or reviewer of the paper might disagree. In that case, change it.
But the paper is yours. Do what you thing makes the most sense and makes the paper accessible to your audience.
Generally speaking, in scientific papers, it is best to avoid figures and tables in the introduction unless it provides an outlook to the goals and design of the study. If it is from a previous study just cite the original source. Figures and tables other than outlook are usually included in data/methods, results, or discussion, but not in abstract or intro. For thesis, the story is different. Introduction of a thesis can sometimes be even a review paper you have published in the past, so figures, tables, videos, etc are all fine unless your school specifies otherwise.
I'd expect at least a couple of figures in the introduction of a master's thesis, more in a doctoral thesis. In either case, in some ways, the more the better, as long as they are genuinely relevant and add to the power of the explanation.
For papers you rarely see much beyond a single panel connected with the introduction, laying out the premise of the main model/approach - either a single panel intro figure, or one panel in the first multi-panel data figure. Be aware that journals might limit the number of tables/figures in a paper.
