Horizontal centering with \subfloat

Instead of using the subfig package and its \subfloat macro, you may want to use the subcaption package and its subfigure environment. Specifically, you could specify six subfigure environments of a given fixed width of, say, 0.4\textwidth and use \centering instructions within each of these environments.

Not having access to your image files, it's not possible to guarantee that the following code will work without a need for further tweaking. In particular, you may need to change the widths of the subfigure environments to accommodate the graphs in the third row of subfigures.

\documentclass[11pt]{article}
\usepackage[demo]{graphicx} % omit 'demo' option in real document
\usepackage{subcaption} % for 'subfigure' environment
\begin{document}
\begin{figure}
\centering

    \begin{subfigure}{0.4\textwidth}
       \centering
       \includegraphics[scale=0.45]{Figures/IncludePyramid_a_reverse.eps}
       \caption{From $n=0$ to $n=-1$}\label{fig:a}
    \end{subfigure}          
    \qquad\qquad\qquad  % spacing between the subfigures
    \begin{subfigure}{0.4\textwidth}  
       \centering
       \includegraphics[scale=0.45]{Figures/IncludePyramid_a.eps}
       \caption{From $n=-1$ to $n=0$}\label{fig:aa}
    \end{subfigure}    

    \begin{subfigure}{0.4\textwidth}
       \centering
       \includegraphics[scale=0.45]{Figures/IncludePyramid_b_reverse.eps}
       \caption{From $n=-1$ to $n=-2$}\label{fig:b}
    \end{subfigure}          
    \qquad\qquad\qquad  % spacing between the subfigures
    \begin{subfigure}{0.4\textwidth}  
       \centering
       \includegraphics[scale=0.45]{Figures/IncludePyramid_b.eps}
       \caption{From $n=-2$ to $n=-1$}\label{fig:bb}
    \end{subfigure}    

    \begin{subfigure}{0.4\textwidth}
       \centering
       \includegraphics[scale=0.45]{Figures/IncludePyramid_c_reverse.eps}
       \caption{From $n=-2$ to $n=-3$}\label{fig:c}
    \end{subfigure}          
    \qquad\qquad\qquad  % spacing between the subfigures
    \begin{subfigure}{0.4\textwidth}  
       \centering
       \includegraphics[scale=0.45]{Figures/IncludePyramid_c.eps}
       \caption{From $n=-3$ to $n=-2$}\label{fig:cc}
    \end{subfigure}    

\caption{Random walk on the Pascal pyramid} \label{fig:bratelli}
\end{figure}
\end{document}

You have to work a bit harder. The following set of macros sets each subfloat in a zero width box, so adding filling space will do.

1. The \csubfloat macro has the same syntax as \subfloat; beware, though, that images should not fill the whole line.

2. The \centerhfill macro has an optional argument, default \quad to add a space in the center. If it's not enough, you can experiment with \centerhfill[\qquad].

In the example I have used the demo option to graphicx; don't use it yourself, but don't add dvips either.

The \fakeig macro is just for producing the test and you don't need it; just remove the lines and uncomment the \includegraphics ones.

\documentclass[11pt]{article}
\usepackage[demo]{graphicx}
\usepackage{subfig}

\newcommand{\csubfloat}[2][]{%
  \makebox[0pt]{\subfloat[#1]{#2}}%
}
\newcommand{\centerhfill}[1][\quad]{\hspace{\stretch{0.5}}#1\hspace{\stretch{0.5}}}

% This is for the example
\newcommand{\fakeig}[2]{\includegraphics[width=#1,height=#2]{foo}}

\begin{document}

\begin{figure}[htp]
  \centering
  \hspace*{\fill}%
  \csubfloat[From $n=0$ to $n=-1$]{\label{fig:a}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_a_reverse.eps}%
    \fakeig{2cm}{2cm}%
  }\centerhfill
  \csubfloat[From $n=-1$ to $n=0$]{\label{fig:aa}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_a.eps}%
    \fakeig{2cm}{2cm}%
  }\hspace*{\fill}

  \hspace*{\fill}%
  \csubfloat[From $n=-1$ to $n=-2$]{\label{fig:b}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_b_reverse.eps}%
    \fakeig{3cm}{3cm}%
  }\centerhfill
  \csubfloat[From $n=-2$ to $n=-1$]{\label{fig:bb}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_b.eps}%
    \fakeig{3cm}{3cm}%
  }\hspace*{\fill}

  \hspace*{\fill}%
  \csubfloat[From $n=-2$ to $n=-3$]{\label{fig:c}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_c_reverse.eps}%
    \fakeig{4cm}{4cm}%
  }\centerhfill
  \csubfloat[From $n=-3$ to $n=-2$]{\label{fig:cc}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_c.eps}%
    \fakeig{4cm}{4cm}%
  }\hspace*{\fill}

  \caption{Random walk on the Pascal pyramid}
  \label{fig:bratelli}
\end{figure}

\end{document}

Note a generous usage of % to mask end-of-lines that act like spaces, which are not wanted.

Another option would be to include each \subfloat in a minipage as wide as half the \textwidth, but you have less control about the center spacing; this could be modified using a fraction of \textwidth, say \begin{minipage}{.8\textwidth} or similar.

\documentclass[11pt]{article}
\usepackage[demo]{graphicx}
\usepackage{subfig}

% This is for the example
\newcommand{\fakeig}[2]{\includegraphics[width=#1,height=#2]{foo}}

\begin{document}

\begin{figure}[htp]
  \centering
  \begin{minipage}{.5\textwidth}\centering
  \subfloat[From $n=0$ to $n=-1$]{\label{fig:a}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_a_reverse.eps}%
    \fakeig{2cm}{2cm}%
  }
  \end{minipage}%
  \begin{minipage}{.5\textwidth}\centering
  \subfloat[From $n=-1$ to $n=0$]{\label{fig:aa}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_a.eps}%
    \fakeig{2cm}{2cm}%
  }
  \end{minipage}

  \begin{minipage}{.5\textwidth}\centering
  \subfloat[From $n=-1$ to $n=-2$]{\label{fig:b}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_b_reverse.eps}%
    \fakeig{3cm}{3cm}%
  }
  \end{minipage}%
  \begin{minipage}{.5\textwidth}\centering
  \subfloat[From $n=-2$ to $n=-1$]{\label{fig:bb}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_b.eps}%
    \fakeig{3cm}{3cm}%
  }
  \end{minipage}

  \hspace*{\fill}%
  \begin{minipage}{.5\textwidth}\centering
  \subfloat[From $n=-2$ to $n=-3$]{\label{fig:c}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_c_reverse.eps}%
    \fakeig{4cm}{4cm}%
  }
  \end{minipage}%
  \begin{minipage}{.5\textwidth}\centering
  \subfloat[From $n=-3$ to $n=-2$]{\label{fig:cc}%
%    \includegraphics[scale=0.45]{Figures/IncludePyramid_c.eps}%
    \fakeig{4cm}{4cm}%
  }
  \end{minipage}

  \caption{Random walk on the Pascal pyramid}
  \label{fig:bratelli}
\end{figure}

\end{document}