drawing commutative diagram

Question

I solved the problem I mentioned below, thank you very much for your suggestions.

I want to use the diagram to appear in the article. I want to set the size according to the article in this example. I do not know whether I could express myself correctly. Thank you for all suggestions.

Could you help me for drawing the following diagram ?

Answer 1

This is not a complete answer to your question. It is just a good example to start with knowing that there are many approaches to your problem.

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{matrix}

\begin{document}

  \begin{tikzpicture}[->,>=stealth]
    \matrix (dag)  [matrix of nodes,%
    nodes={rectangle,draw},
    column sep={2cm,between origins},
    row sep={2cm,between origins},
    ampersand replacement=\&] {
        \& |(1)| Start  \&                                  \\
        |(11)| A            \& |(12)| B     \& |(13)| C \\
      \& |(21)| End         \&                                  \\
    };

    \draw (1) to (11);
    \draw (1) to (12);
    \draw (1) to (13);
    \draw (11) to (12);
    \draw (12) to (13);
    \draw (11) to (21);
    \draw (12) to (21);
    \draw (13) to (21);
  \end{tikzpicture}

\end{document}

---

Edit

I am not the TikZpert here in the slightest, but I spent some time converting your hand drawing into a simple code. Please, study it well since do-it-for-me questions are the most hated ones here :).

\documentclass[12pt]{article}

\usepackage{tikz}
\usetikzlibrary{matrix}

\begin{document}
\begin{figure}
  \begin{tikzpicture}[->,>=stealth,]
    \matrix (dag)  [matrix of nodes,%
    nodes={rectangle,draw},
    column sep={3ex},
    row sep={10ex,between origins},
    ampersand replacement=\&] {
        \& |(01)| $\sigma$-rigid  \& \\
        |(11)| strongly $\sigma$-symmetric \& |(12)| strongly symmetric  \& |(13)| symmetric \\
        |(21)| strongly $\sigma$-skew reversible \& |(22)| strongly reversible  \& |(23)| reversible \\
        |(31)| strongly $\sigma$-IFP \& |(32)| strongly IFP  \& |(33)| IFP \\
      \& |(41)| Abelian \&  \\
    };



    \draw (01.south west) -- (11.north east); \draw (01) -- (12); \draw (01.south east) -- (13.north west);
    \draw[<->] (11) -- node[midway,right]{text} (21); \draw (21) -- (31); \draw (31.south east) -- (41.north west);
    \draw (12) -- (22); \draw (22) to (32); \draw (32) -- (41);
    \draw[<->] (13) -- (23); \draw (23) -- (33); \draw (33.south west) -- (41.north east);

    \draw (11) -- (12); \draw (12) -- (13); \draw (12) -- (13);
    \draw (21) -- (22); \draw (22) -- (23); \draw (22) -- (23);
    \draw (31) -- node[above] {dummy} (32); \draw (32) -- (33); \draw (32) -- (33);


  \end{tikzpicture}
\end{figure}
\end{document}