First of all, let me say I'm using LyX, though I have no problem using ERT.
Secondly, what is the most simplest way to draw a simple graph like this in Latex?
I've seen some documents with graphs and I've seen some examples, but I couldn't figure out how to just draw a simple graph - what packages do I need, etc?
We can now discuss the packages that we can use to draw graphs in LaTeX. The most common LaTeX package used for drawing, in general, is TikZ, which is a layer over PGF that simplifies its syntax.
TikZ can do this.
A quick demo:
\documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} [scale=.8,auto=left,every node/.style={circle,fill=blue!20}] \node (n6) at (1,10) {6}; \node (n4) at (4,8) {4}; \node (n5) at (8,9) {5}; \node (n1) at (11,8) {1}; \node (n2) at (9,6) {2}; \node (n3) at (5,5) {3}; \foreach \from/\to in {n6/n4,n4/n5,n5/n1,n1/n2,n2/n5,n2/n3,n3/n4} \draw (\from) -- (\to); \end{tikzpicture} \end{document}
produces:
More examples @ http://www.texample.net/tikz/examples/tag/graphs/
More information about TikZ: http://sourceforge.net/projects/pgf/ where I guess an installation guide will also be present.
Aside from the (excellent) suggestion to use TikZ, you could use gastex. I used this before TikZ was available and it did its job too.
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