diff --git a/tests/position.tex b/tests/position.tex
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--- a/tests/position.tex
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-%!TEX root = ../main.tex
-
-\subsection{Influence of receiver position on costs}
-\newcommand{\gbcns}{\mathcal{C}}
-
-One distinguishing feature of networks where player costs have improved after the suggestion is that the seeds advise to play a best response for a larger fraction of time. However, there is not a significantly higher fraction of receivers for which the seed is their current colour choice in the two successful networks. But by the end of the round, in \textit{ba} and \textit{ws}, a significantly larger fraction of receivers never deviated from the suggestion than in \textit{er} and \textit{sb}. In other words, their environment maintained the seed as a best response.
-
-The preceding observation indicates that network effects are at play, such as the topology of the graphs and the position of the receivers.
-The group betweenness centrality \citep{everett_centrality_1999} of a set of nodes is employed here to explain the qualitatively different results obtained in the four networks. Let \( \gbcns \) be a set of nodes in the network. Their group betweenness centrality (GBC) is measured by the sum over all pairs of sources and destinations \( s, \, t \) (not included in \( \gbcns \)) of the fraction of shortest paths connecting \( s \) to \( t \) running through at least one point in \( \gbcns \) among all shortest paths connecting \( s \) to \( t \).
-% \[
-% 	\text{GBC}(\gbcns) = \sum_{s,t \notin \gbcns} \frac{\sigma^*_{s,t}(\gbcns)}{\sigma_{s,t}}
-% \]
-
-\begin{figure}
-  \centering
-	\begin{subfigure}[t]{0.45\linewidth}
-    \centering
-	  \includegraphics[width=\linewidth]{Coloring/Figures/wslowgbc}
-    \caption{}
-  \end{subfigure}
-	\hfill
-  \begin{subfigure}[t]{0.45\linewidth}
-    \centering
-  	\includegraphics[width=\linewidth]{Coloring/Figures/wshighgbc}
-    \caption{}
-  \end{subfigure}
-  \caption{Comparison of the group betweenness centrality of two sets of receivers with the sum of their individual betweenness centralities \( \Sigma_b \). The GBC more accurately measures the centrality of the set of receivers.
-	\textbf{a.}~GBC = \( 63.84 \), \( \Sigma_b = 300.57 \).
-	\textbf{b.}~GBC = \( 240.43 \), \( \Sigma_b = 286.8 \).}
-  \label{fig:gbccomp}
-\end{figure}
-
-We compare in Figure \ref{fig:gbccomp} the GBC of a set of nodes with the sum of their individual betweenness centralities. The latter does not discriminate between a highly clustered set of receivers, for which the seeds may only have local effects, and a set that covers more appropriately the network. This is unlike the GBC which gives a starkly different measure for both sets, and is thus a relevant metric for the effect of receiver positions.
-
-We test this hypothesis by sampling at random \( k \) receivers on the network. A dynamics is run until an equilibrium is reached, at which point a colouring is selected in the same manner as in the game. The \( k \) receivers immediately update to the seed, and the dynamics is run again until a new equilibrium \( S_f \) is reached. We repeat this procedure for \( m \) times and average the number of matches obtained in \( S_f \). The set of receivers is sampled \( n \) times, for \( k = \{3, 6\} \) and we compare the series of receivers' GBC with the corresponding average number of matches, using Spearman's rank correlation coefficient. The full table of results is presented in Table \ref{tab:col/gbcsim}.
-
-\begin{table}
-  \centering
-  \caption{Spearman rank correlation coefficient between group betweenness centrality and average number of matches at final equilibrium, for each network and communication level. Significance levels are given next to the values: (*) \( p < 0.05 \), (**) \( p < 0.01 \), (***) \( p< 0.001 \).
-  Best response dynamics are run by sampling one node at a time and choosing at random a best response, until all nodes are at equilibrium.
-  As suggestions are sent, receivers follow the seed unconditionally. Multiplicative weight updates (MWU) keeps track of the players' mixed strategies.
-  Finally, we test the correlation between the GBC of the set of receivers and the average player cost for simulations based on the behavioural model of players.
-  Each dynamics is run for \( n \) times on \( m \) random receiver sets.
-  }
-  \label{tab:col/gbcsim}
-  \begin{tabular}{l|l|llll}
-  & & \multicolumn{4}{c}{Networks} \\
-  \midrule
-  Dynamics & Receivers & ba & ws & er & sb \\
-  \midrule
-  \multirow{2}{*}{\shortstack[l]{BR \\ \( (n = 200, m = 100) \)}} & 10\% &
-      -0.355 (***) & -0.215 (**) & -0.144 (*) & -0.107 \\
-    & 20\% & -0.449 (***) & -0.137 & -0.279 (***) & -0.391 (***) \\
-  \midrule
-  \multirow{2}{*}{\shortstack[l]{MWU \\ \( (n = 100, m = 100) \)}} & 10\% &
-      -0.220 (*) & -0.282 (**) & 0.007 & -0.166 \\
-    & 20\% & -0.119 & -0.112 & -0.099 & 0.113 \\
-  \midrule
-  & & & & & \\
-  \midrule
-  \multirow{2}{*}{\shortstack[l]{Behavioural model \\ \( (n = 200, m = 100) \)}} & 10\% &
-      -0.549 (***) & -0.176 (*) & -0.363 (***) & -0.419 (***) \\
-    & 20\% & -0.592 (***) & -0.236 (***) & -0.352 (***) & -0.553 (***) \\
-  \bottomrule
-  \end{tabular}
-\end{table}
-
-With best response (BR) dynamics, for almost all networks and all values of \( k \), the coefficient is significantly smaller than 0, indicating that a higher GBC translates to a lower average number of matches. The dynamics is obtained by sampling uniformly at random one node at a time and allowing this node to play her current best response strategy, or one of them in case of ties.
-
-The results are more contrasted with multiplicative weight update (MWU) dynamics \citep{littlestone1994weighted}, perhaps reflecting the noisier approach of the procedure. The dynamics is carried over mixed strategies of the agents, or probability distribution over their colour choices. At each step, every player's mixed strategy is updated by decreasing the probability of a colour that yields a higher cost against the expected choice of one's neighbours.
-
-Finally, a behavioural model obtained from the experimental data (detailed in \ref{sec:col/simdef}) yields strong indication that the GBC of receivers is inversely correlated with the average of all player costs, computed with the same experimental scoring function. The model is obtained from two logistic regressions encoding respectively the choice to deviate from one's current action and the subsequent colour choice.
-
-\begin{figure}
-  \centering
-  \includegraphics[width=0.7\linewidth]{Coloring/Figures/netcorr-box.pdf}
-  \caption{Spearman correlation coefficient for networks of 20 nodes and three dynamics (BR, MWU, behavioural model). For each network, 25 sets of 2 and 4 receivers are selected randomly. For each set of receivers, each dynamics is simulated 50 times and its resulting statistic is computed, the average number of matches for BR and MWU and the resulting average player cost for the behavioural model. The correlation is obtained for each network between the GBC of the receiver set and the resulting statistic. The boxplot represents the distribution of these coefficients for each network family and number of receivers. For most networks, the correlation coefficient is significantly below 0, indicating that more central receivers (as measured by the GBC) tend to improve the play.}
-	\label{fig:netgbc}
-\end{figure}
diff --git a/tests/topology.tex b/tests/topology.tex
deleted file mode 100644
index 358d305..0000000
--- a/tests/topology.tex
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-%!TEX root = ../main.tex
-
-\begin{figure}
-  \centering
-  \includegraphics[width=0.7\linewidth]{Coloring/Figures/netstatcorr.pdf}
-  \caption{Scatterplot of the measure of cost for each dynamics (average resulting number of matches for BR and MWU, average player cost for the behavioural model). Simulations with 2 or 4 receivers appear on the same plot. Values of the network statistics and cost are rescaled for plotting (no incidence on the Spearman correlation coefficient). As either the average distance or the clustering coefficient of the network increases, the cost increases.}
-	\label{fig:netstatcorr}
-\end{figure}
-
-\subsection{Influence of network topology on costs}
-The three dynamics are repeated on 80 networks, 20 per type, with 20 nodes each. The additional networks were generated from the same rules which yielded the four networks in the study. For each of these networks, 25 sets of receivers were sampled randomly for \( k = \{2, 4\} \). For each set of receivers, the three dynamics were sampled from 50 times to obtain the average number of matches resulting from BR and MWU or the average player cost from the behavioural model. Once again, the correlation between these statistics and the centrality of the receivers were computed and shown to be significantly negative for most networks.
-
-Figure \ref{fig:netgbc} charts the distribution of these correlation coefficients for the two experimental conditions and each of the four types. Again, contrasts exist between the four different types. Preferential attachment networks such as \textit{ba} have the strongest negative correlation between centrality and efficiency of the suggestion. On the other hand, over half of Watts-Strogatz networks have a positive correlation for the behavioural model simulations with 2 receivers and typically do not feature as strong negative correlations as the three other types in remaining treatments.
-
-The differences are explained by the topology of the networks, as measured by network statistics such as the clustering coefficient or the average distance between two vertices. On the same set of 80 networks, a strong negative correlation is found between any of the two previous statistics and cost (Figure \ref{fig:netstatcorr} and Table \ref{tab:col/gennetcor}). Thus, a more clustered network leads to increased cost, as does a network with larger average distance. Watts-Strogatz networks, among the four considered types, are indeed more clustered and have higher average distance than any other type (Table \ref{tab:col/gennetstat}).
-
-\begin{table}\centering
-  \caption{Spearman rank correlation coefficient between one network statistic (average distance or clustering coefficient) and a measure of system inefficiency (average number of matches for BR and MWU, average player cost for the behavioural model), for each simulated dynamics.
-  Simulations were carried over 80 networks of 20 nodes each, 20 networks per type. 25 receiver sets were sampled for each network at sizes 2 and 4 (resp. 10\% and 20\% of nodes), with each dynamics run for 50 times on each set. Averages are obtained over all receiver sets.
-  Significance levels are given next to the values: (*) \( p < 0.05 \), (**) \( p < 0.01 \), (***) \( p< 0.001 \).}
-  \label{tab:col/gennetcor}
-  \begin{tabular}{l|l|l}
-  \toprule
-  Dynamics & Statistic & Correlation \\
-  \midrule
-  \multirow{2}{*}{BR} & Average distance & 0.647 (***) \\
-    & Clustering coefficient & 0.628 (***) \\
-  \midrule
-  \multirow{2}{*}{MWU} & Average distance & 0.362 (***) \\
-    & Clustering coefficient & 0.207 (**) \\
-  \midrule
-  & & \\
-  \midrule
-  \multirow{2}{*}{Behavioural model} & Average distance & 0.681 (***) \\
-    & Clustering coefficient & 0.628 (***) \\
-  \bottomrule
-  \end{tabular}
-\end{table}
-
-\begin{table}\centering
-  \caption{Average network statistics (average distance and clustering coefficient) for 80 additional generated networks, 20 per types.}
-  \label{tab:col/gennetstat}
-  \begin{tabular}{l|l|l}
-  \toprule
-  Network & Average distance & Clustering coefficient \\
-  \midrule
-  ba & 2.12 & 0.208 \\
-  \midrule
-  ws & 2.42 & 0.342 \\
-  \midrule
-  er & 2.20 & 0.194 \\
-  \midrule
-  sb & 2.23 & 0.180 \\
-  \bottomrule
-  \end{tabular}
-\end{table}