Why does the same code give two different outputs?

Question

I accidentally copied and pasted the same code right below it. But the output is different. The second one has a strange omega attached to the triangle inside the set. Why is that? I copied it right below it again, and the omega shows up again. Based on the code, shouldn't the output be the same? Here is the code (credit to the second solution to my post here https://tex.stackexchange.com/a/653535/8650). Thanks in advance!

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary {graphs}
\usetikzlibrary{quotes}
\tikzgraphsset{
empty nodes,
nodes={circle, draw, inner sep=0pt, minimum size=2pt},
counterclockwise, radius=6pt, phase=210,
}
\tikzset{
baseline=-2pt,
every label/.style={font=\tiny, inner sep=0pt},
dashed/.style={dash pattern=on 1pt off 1pt},
label distance=1pt,
}

\begin{document}

Let $\mathcal{H}$ be \{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\} and $\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};

Let $\mathcal{H}$ be \{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\} and $\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};


\end{document}

Edit: Here is a screenshot of the output

Edit: code from https://tex.stackexchange.com/a/653535/277998

Answer 1

Looks like you have some typos in your two lines of content. First I split one line, to better localize the errors the compiler flagged, and commented out the second (your copy). Second, I corrected and copied the "new" content.

Just compare "your" and "my" tikz-statements; i.e. just use it like any other call to a macro (e.g. defined by a \newcommand) in running text:

\{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\}% yours

\tikz{\graph[n=3]{1,2,3;1--2,1--3,2--3}}% mine

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary {graphs}
\usetikzlibrary{quotes}
\tikzgraphsset{
empty nodes,
nodes={circle, draw, inner sep=0pt, minimum size=2pt},
counterclockwise, radius=6pt, phase=210,
}
\tikzset{
baseline=-2pt,
every label/.style={font=\tiny, inner sep=0pt},
dashed/.style={dash pattern=on 1pt off 1pt},
label distance=1pt,
}

\begin{document}

Let $\mathcal{H}$ be 
\tikz{\graph[n=3]{1,2,3;1--2,1--3,2--3}} 
and $\sigma$ be 
\tikz{\graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};}


Let $\mathcal{H}$ be 
\tikz{\graph[n=3]{1,2,3;1--2,1--3,2--3}} 
and $\sigma$ be 
\tikz{\graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};}

%Let $\mathcal{H}$ be \{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\} and $\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};


\end{document}

Answer 2

A \tikz command should be delimited by a corresponding ;.

What happens with your code is that the first \tikz instruction is not properly delimited. I slightly reformatted the code (but this is not influential and just allows to be able to see the entire code on the screen)

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary {graphs}
\usetikzlibrary{quotes}

\tikzgraphsset{
  empty nodes,
  nodes={circle, draw, inner sep=0pt, minimum size=2pt},
  counterclockwise, radius=6pt, phase=210,
}
\tikzset{
  baseline=-2pt,
  every label/.style={font=\tiny, inner sep=0pt},
  dashed/.style={dash pattern=on 1pt off 1pt},
  label distance=1pt,
}

\begin{document}

Let $\mathcal{H}$ be \{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\} and 
$\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};

Let $\mathcal{H}$ be \{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\} and 
$\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};

\end{document}

When running LaTeX and going past errors we get

! Package tikz Error: Giving up on this path. Did you forget a semicolon?.

See the tikz package documentation for explanation.
Type  H <return>  for immediate help.
 ...

l.20 ...{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\}
                                                   and
?

! Package tikz Error: Giving up on this path. Did you forget a semicolon?.

See the tikz package documentation for explanation.
Type  H <return>  for immediate help.
 ...

l.23 ...{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3}\}
                                                   and
?

so you clearly see that something goes wrong with the first appearance of the graph in both paragraphs.

I guess that the Omega appears in the second instance because TikZ has been left in an unstable state. It has to do several global settings, and errors in one tikzpicture might lead to unexpected output in following ones. Why Omega? It's the character that sits at slot "0A in the standard font; something was left behind and the strange character appears (an Omega used to show in some Xy-pic diagrams, due to a bug, for instance).

If you switch to T1-encoded fonts the output is

(after the two error messages).

The conclusion is: never disregard error messages and terminate properly \tikz.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary {graphs}
\usetikzlibrary{quotes}

\tikzgraphsset{
  empty nodes,
  nodes={circle, draw, inner sep=0pt, minimum size=2pt},
  counterclockwise, radius=6pt, phase=210,
}
\tikzset{
  baseline=-2pt,
  every label/.style={font=\tiny, inner sep=0pt},
  dashed/.style={dash pattern=on 1pt off 1pt},
  label distance=1pt,
}

\begin{document}

Let $\mathcal{H}$ be \{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3};\} and
$\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};

Let $\mathcal{H}$ be \{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3};\} and
$\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};

\end{document}

Note ;\}. No error and expected output. On the other hand, you should use math mode braces:

Let $\mathcal{H}$ be $\{\tikz \graph[n=3]{1,2,3;1--2,1--3,2--3};\}$ and
$\sigma$ be \tikz \graph[n=2, phase = 180] {1,2;2["2"'right],1["1"'left];1--2};

but it's a different concern.