\section{Clustering
  of~\cite{baldockSystemsApproachReveals2019a,baldockDailyTemporalStructure2011}}

\cite{baldockSystemsApproachReveals2019a} study the diversity, robustness and
impact of the type of environment on the ecological aspect of plant-pollinator
networks in four major english cities. The networks are presented in
figures~\ref{subfig:baldock-english-network-bristol} to~\ref{subfig:baldock-english-network-reading}

\cite{baldockDailyTemporalStructure2011} aim to study the daily temporal
structure in a savanna pollination network. The data was collected in 2004
and in two sites, \emph{Turkana Boma} (TB) and \emph{Junction} (JN) in Kenya.
We will not look for a temporal structure but only use the full networks merged
in one
due to their small sizes. The network obtained is presented in
figure~\ref{fig:baldock-african-networks}.

\emph{Note:} those networks were extracted from a bigger dataset
from~\cite{doreRelativeEffectsAnthropogenic2021}. The full dataset was also
clusterized but issues arose that are discussed in
sub-section~\ref{ssec:difficulties-encountered}.

\begin{figure}[ht]
  \centering
  \begin{subfigure}[htb]{0.47\textwidth}
    \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Bristol}
    \caption{Bristol}
    \label{subfig:baldock-english-network-bristol}
  \end{subfigure}
  \hfill
  \begin{subfigure}[htb]{0.47\textwidth}
    \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Edinburgh}
    \caption{Edinburgh}
  \end{subfigure}
  \newline
  \begin{subfigure}[htb]{0.47\textwidth}
    \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Leeds}
    \caption{Leeds}
  \end{subfigure}
  \hfill
  \begin{subfigure}[htb]{0.47\textwidth}
    \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Reading}
    \caption{Reading}
    \label{subfig:baldock-english-network-reading}
  \end{subfigure}
  \caption{English networks from~\cite{baldockSystemsApproachReveals2019a}}
  \label{fig:baldock-english-networks}
\end{figure}

\begin{figure}[ht]
  \centering
  \includestandalone[width=0.43\textwidth]{tikz/applications/baldock/graph-Baldock2011_TB+Baldock2011_JN}
  \caption{African network from~\cite{baldockDailyTemporalStructure2011}}
  \label{fig:baldock-african-networks}
\end{figure}

We applied our clustering method on those 6 networks, using the four models.
Interesting results arose from \emph{iid} and $\pi\rho$ models, which are
presented below in figures~\ref{fig:baldock-clust-iid}
and~\ref{fig:baldock-clust-pirho}.

\begin{figure}
  \begin{minipage}{.5\textwidth}
    \begin{subfigure}[htb]{\textwidth}
      \includestandalone{tikz/applications/baldock/iid-clust-struct}
      \caption{$\bm{\alpha}$ structures of the\newline
        collections identified}
      \label{subfig:baldock-clust-iid-struct}
    \end{subfigure}
    \newline
    \begin{subfigure}[htb]{\textwidth}
      \includestandalone{tikz/applications/baldock/iid-clust-tree}
      \caption{Tree of splits}
      \label{subfig:baldock-clust-iid-split}
    \end{subfigure}
    \captionof{figure}{Results for \emph{iid} clustering}
    \label{fig:baldock-clust-iid}
  \end{minipage}%
  \begin{minipage}{.5\textwidth}
    \begin{subfigure}[htb]{\textwidth}
      \includestandalone{tikz/applications/baldock/pirho-clust-struct}
      \caption{$\bm{\alpha}$ structure of the\newline
        collection identified}
      \label{subfig:baldock-clust-pirho-struct}
    \end{subfigure}
    \newline
    \begin{subfigure}[htb]{\textwidth}
      \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/pirho-clust-tree}
      \caption{Tree of splits}
      \label{subfig:baldock-clust-pirho-split}
    \end{subfigure}
    \captionof{figure}{Results for $\pi\rho$ clustering}
    \label{fig:baldock-clust-pirho}
  \end{minipage}
\end{figure}

\paragraph{Results} The main thing one can see when comparing the two
clusterings is that while \emph{iid} do not find a common structure, $\pi\rho$
manage to find one.