How to draw a graph in LaTeX?

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?

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.

I have used graphviz ( https://www.graphviz.org/gallery ) together with LaTeX using dot command to generate graphs in PDF and includegraphics to include those.

If graphviz produces what you are aiming at, this might be the best way to integrate: dot2tex: https://ctan.org/pkg/dot2tex?lang=en

Perhaps use tikz.

In my experience, I always just use an external program to generate the graph (mathematica, gnuplot, matlab, etc.) and export the graph as a pdf or eps file. Then I include it into the document with includegraphics.