[Tex/LaTex] Fail to add caption to the right side of subfigures

beamercaptionsfloatssubcaption

I am trying to place the captions on the right side of each subfigures in Beamer. I'd like to be a 2*2 figure; in each subfigure its subcaption be on the right side of that subfigure with more text to explain that subfigure. Hence, it will be a figure with 4 subfigures and 4 subcaptions. Thanks.

Edited code after solution of @Mico's solution for more adjustment:

  \documentclass[demo]{beamer}
    \setbeamertemplate{caption}[numbered]% <-- added, for other option see beamer manual, page 124
    \usepackage{subcaption}

    \begin{document}
    \begin{frame}
    \begin{figure}

        \captionsetup[subfigure]{labelformat=empty}
         \begin{subfigure}{0.7\textwidth}
              \flushleft
              \begin{minipage}{0.5\linewidth}
                  \includegraphics[width=\textwidth]{Fig4}
              \end{minipage}
              \begin{minipage}{0.45\linewidth}
                  \caption{\tiny{Biological Networks: }}
                  \label{fig:BiologicalNetworks}
              \end{minipage}
          \end{subfigure}
    \hfill
         \begin{subfigure}{0.5\textwidth}
            \begin{minipage}{0.5\linewidth}
                \includegraphics[width=\textwidth]{Fig1}
            \end{minipage}
            \begin{minipage}{0.45\linewidth}
                 \caption{\tiny{Social Networks: }}
                 \label{fig:SocialNetworks}
            \end{minipage}
         \end{subfigure}

    \caption{Examples of graph data modelling}
    \label{fig:GraphModelling}
    \end{figure}

    \end{frame}
    \end{document}

Best Answer

If you want to place the captions of the subfigures to the right, rather than below, of the graphs, you need to encase the graphs and caption instructions in separate minipage environments -- and allow for the space taken up by the captions.

Judging by the look of the following screenshot, I don't think you're doing your readers a favor with this setup.

enter image description here

\documentclass[demo]{beamer}
\setbeamertemplate{caption}[numbered]% <-- added, for other option see beamer manual, page 124
\usepackage{subcaption}

\begin{document}
\begin{frame}
\begin{figure}

\begin{subfigure}{0.45\textwidth}
\begin{minipage}{0.5\linewidth}
\includegraphics[width=\textwidth]{Fig4}
\end{minipage}\hfill
\begin{minipage}{0.45\linewidth}
\caption{Social Networks}
\label{fig:SocialNetworks}
\end{minipage}
\end{subfigure}
\hfill
\begin{subfigure}{0.45\textwidth}
\begin{minipage}{0.5\linewidth}
\includegraphics[width=\textwidth]{Fig4}
\end{minipage}\hfill
\begin{minipage}{0.45\linewidth}
\caption{Energy Networks}
\label{fig:EnergyNetworks}
\end{minipage}
\end{subfigure}

\caption{Examples of graph data modelling}
\label{fig:GraphModelling}
\end{figure}

See image \ref{fig:SocialNetworks} in figure \ref{fig:GraphModelling}.
\end{frame}
\end{document}

Addendum: I would adapt your second code batch as follows:

enter image description here

\documentclass[demo]{beamer}
\setbeamertemplate{caption}[numbered]
\usepackage{subcaption,ragged2e}

\begin{document}
\begin{frame}[t] % <--- for top alignment
\begin{figure}
\captionsetup[subfigure]%
     {labelformat=empty,justification=RaggedRight}

\begin{subfigure}{0.475\textwidth}
\begin{minipage}{0.55\linewidth}
\includegraphics[width=\textwidth]{Fig4}
\end{minipage}\hfill
\begin{minipage}{0.42\linewidth}
\caption{\tiny Biological Networks: Agent based brain models for the resting state brain; Karen Joyce, Satoru Hayasaka and Paul Laurienti}
\label{fig:BiologicalNetworks}
\end{minipage}
\end{subfigure}%
\hfill % maximize space between the subfigures
\begin{subfigure}{0.475\textwidth}
\begin{minipage}{0.55\linewidth}
\includegraphics[width=\textwidth]{Fig1}
\end{minipage}\hfill
\begin{minipage}{0.42\linewidth}
\caption{\tiny Social Networks: Data: AER, JPE, Econometrica, RES, QJE (2000--present). By~Cloudly. From: www.cloudlychen.net (the higher level of connections with others)}
\label{fig:SocialNetworks}
\end{minipage}
\end{subfigure}

\caption{Examples of graph data modelling}
\label{fig:GraphModelling}
\end{figure}
A cross-reference to Figure \ref{fig:BiologicalNetworks}.
\end{frame}
\end{document}
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