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}

```