Tikz, subfigure and caption

Question

I am trying to draw some knots side by side with tikz, the label them, but it just doesn't work with my code. I use the package: caption, subcaption, tikz (knots).

\usepackage[utf8]{inputenc}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{tikz}
\usetikzlibrary{matrix, arrows, knots}
\usepackage{graphicx}

\begin{document}
  \begin{figure}
    \begin{subfigure}[b]{0.45\textwidth}
      \centering
        \resizebox{\linewidth}{!}{           
          \begin{tikzpicture}
            \foreach \brk in {0,1,2} {
            \begin{scope}[rotate=\brk * 120]
            \node[knot crossing, transform shape,
            inner sep=1.5pt] (k\brk) at (0,-1) {};
            \end{scope}
            }
            \foreach \brk in {0,1,2} {
            \pgfmathparse{int(Mod(\brk - 1,3))}
            \edef\brl{\pgfmathresult}
            \draw[thick,red] (k\brk) .. controls (
            k\brk.4 north west) and (k\brl.4 north east) .. (k\brl.center);
            \draw[thick,red] (k\brk.center) .. controls (k\brk.16 south west) and (k\brl.16 south east) .. (k\brl);
            }
        \end{tikzpicture}
      }
    \caption{Trefoil}
    \label{a}
   \end{subfigure}
   \begin{subfigure}[b]{0.45\textwidth}
      \centering
        \resizebox{\linewidth}{!}{ 
          \begin{tikzpicture}
            \def\foil{3}
            \foreach \brk in {1,...,\foil} {
            \begin{scope}[rotate=\brk * 360/\foil]
            \node[transform shape, knot crossing, inner sep=1.5pt] (k\brk) at (0,-1) {};
            \end{scope}
            }
            \draw[thick,red] (0,0) \foreach \brk in {1,...,\foil} {let \na=\brk, \nb={int(Mod(\brk,\foil)+1)}, \nc={int(Mod(\brk+1,\foil)+1)} in (k\na) .. controls (k\na.16 south east) and (k\nb.16 south west) .. (k\nb.center) .. controls (k\nb.4 north east) and (k\nc.4 north west) .. (k\nc)};
          \end{tikzpicture}
        }
        \caption{Cinquefoil}
        \label{b}
      \end{subfigure}
    \end{figure}
  \caption{Examples of knots} 
  \end{figure}
\end{document}

Answer 1

As mentioned in comments, your code has several errors: no document class, an extra \end{figure}, misuse of the let PGF syntax and failure to include the calc library which that requires. (You include several things not required to get your example compiling, but omit several which are needed.)

That said, once those errors are fixed, the two figures seem to be resized similarly. Indeed, they appear identical.

My best guess is that you are continuing compilation despite errors with predictably unwanted results. Even warnings should not be simply ignored. Errors need fixing. TeX is telling you that things have gone wrong and it cannot figure out what to do. Generally, it will try to do something if you insist, but this is not aimed at producing the intended output. It is aimed at possibly providing useful information for debugging purposes.

\documentclass{article}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{tikz}
\usetikzlibrary{knots,calc}
\begin{document}
\begin{figure}
  \begin{subfigure}[b]{0.45\textwidth}
    \centering
    \resizebox{\linewidth}{!}{
      \begin{tikzpicture}
        \foreach \brk in {0,1,2} {
          \begin{scope}[rotate=\brk * 120]
            \node[knot crossing, transform shape,
            inner sep=1.5pt] (k\brk) at (0,-1) {};
          \end{scope}
        }
        \foreach \brk in {0,1,2} {
          \pgfmathparse{int(Mod(\brk - 1,3))}
          \edef\brl{\pgfmathresult}
          \draw[thick,red] (k\brk) .. controls (
          k\brk.4 north west) and (k\brl.4 north east) .. (k\brl.center);
          \draw[thick,red] (k\brk.center) .. controls (k\brk.16 south west) and (k\brl.16 south east) .. (k\brl);
        }
      \end{tikzpicture}
    }
    \caption{Trefoil}
    \label{a}
  \end{subfigure}
  \begin{subfigure}[b]{0.45\textwidth}
    \centering
    \resizebox{\linewidth}{!}{
      \begin{tikzpicture}
        \def\foil{3}
        \foreach \brk in {1,...,\foil} {
          \begin{scope}[rotate=\brk * 360/\foil]
            \node[transform shape, knot crossing, inner sep=1.5pt] (k\brk) at (0,-1) {};
          \end{scope}
        }
        \draw[thick,red] (0,0) \foreach \brk in {1,...,\foil} {let \n0=\brk, \n1={int(Mod(\brk,\foil)+1)}, \n2={int(Mod(\brk+1,\foil)+1)} in (k\n0) .. controls (k\n0.16 south east) and (k\n1.16 south west) .. (k\n1.center) .. controls (k\n1.4 north east) and (k\n2.4 north west) .. (k\n2)};
      \end{tikzpicture}
    }
    \caption{Cinquefoil}
    \label{b}
  \end{subfigure}
\caption{Examples of knots}
\end{figure}
\end{document}