@@ 1208,6 1208,15 @@ were manually merged within Gephi.
Gephi allows some graph properties to be analysed, including the degree
distribution of nodes and (weighted) clustering coefficient.
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth]{midlands2002-2008/degree.png}
+ \caption{Degree distribution of the East Midlands funding network
+ (2002 to 2008), where nodes are organisations and edges are projects
+ those organisations are collaborating on.}
+ \label{fig:midlands2002_2008Degree}
+\end{figure}
+
The degree distribution shown in figure \ref{fig:midlands2002_2008Degree} is
similar to that of the network as a whole (see [Amount of research]), with the
vast majority of nodes (i.e. organisations) having a low number of connections,
@@ 1222,6 1231,16 @@ that publicly funded research in the East Midlands region does not stand out
significantly from other regions in terms of amount of research and its
distribution.
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth]{midlands2002-2008/weightedDegree.png}
+ \caption{Weighted degree distribution of the East Midlands funding
+ network (2002-2008), where nodes are organisations, edges are projects
+ those organisations are collaborating on, and the weight of edges is the
+ total spent on the project between both organisations.}
+ \label{fig:midlands2002_2008WeightedDegree}
+\end{figure}
+
The weighted degree distribution (where each edge is multiplied by its weight)
for the graph is shown in figure \ref{fig:midlands2002_2008WeightedDegree},
where the weight is the cost of the project between the two organisations.
@@ 1229,6 1248,18 @@ A similar pattern is shown to the degree distribution; lower values have
significantly greater frequencies, and higher costs becoming rarer as indicated
by the sparsity at higher values.
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth]{midlands2002-2008/clustering.png}
+ \caption{Clustering coefficient distribution of the East Midlands funding
+ network (2002 to 2008), where nodes are organisations and edges are projects
+ those organisations are collaborating on.
+ It shows that organisations are much more likely to only be involved in a
+ few collaborations, and organisations with high amounts of collaboration
+ are few and far between.}
+ \label{fig:midlands2002_2008Clustering}
+\end{figure}
+
The clustering coefficient is a measure of "the degree to which nodes tend to
cluster together" (@opsahl2009clustering), originally attempted by
@luce1949method.
@@ 1336,6 1367,18 @@ top degree is 172 compared to 2002 to 2008's 114. This suggests a lower amount o
collaboration from most organisations in this later time period, but the top
organisations are involved in more.
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth]{nodeXLDegrees}
+ \caption{Degree distribution of the East Midlands funding network
+ (2005-2010), where nodes are organisations and edges are projects
+ those organisations are collaborating on.
+ It shows that organisations are much more likely to only be involved in
+ a few collaborations, and organisations with high amounts of
+ collaboration are few and far between.}
+ \label{fig:midlands2005_2010Degree}
+\end{figure}
+
### Visualisation
Nodes were scaled by the number of project connections they had within that time
@@ 2304,49 2347,6 @@ Projects that are related to one another in some way.
\label{fig:midlands2002_2008}
\end{sidewaysfigure}
-\begin{figure}
- \centering
- \includegraphics[width=0.7\textwidth]{midlands2002-2008/degree.png}
- \caption{Degree distribution of the East Midlands funding network
- (2002 to 2008), where nodes are organisations and edges are projects
- those organisations are collaborating on.}
- \label{fig:midlands2002_2008Degree}
-\end{figure}
-
-\begin{figure}
- \centering
- \includegraphics[width=0.7\textwidth]{midlands2002-2008/weightedDegree.png}
- \caption{Weighted degree distribution of the East Midlands funding
- network (2002-2008), where nodes are organisations, edges are projects
- those organisations are collaborating on, and the weight of edges is the
- total spent on the project between both organisations.}
- \label{fig:midlands2002_2008WeightedDegree}
-\end{figure}
-
-\begin{figure}
- \centering
- \includegraphics[width=0.7\textwidth]{midlands2002-2008/clustering.png}
- \caption{Clustering coefficient distribution of the East Midlands funding
- network (2002 to 2008), where nodes are organisations and edges are projects
- those organisations are collaborating on.
- It shows that organisations are much more likely to only be involved in a
- few collaborations, and organisations with high amounts of collaboration
- are few and far between.}
- \label{fig:midlands2002_2008Clustering}
-\end{figure}
-
-\begin{figure}
- \centering
- \includegraphics[width=0.7\textwidth]{nodeXLDegrees}
- \caption{Degree distribution of the East Midlands funding network
- (2005-2010), where nodes are organisations and edges are projects
- those organisations are collaborating on.
- It shows that organisations are much more likely to only be involved in
- a few collaborations, and organisations with high amounts of
- collaboration are few and far between.}
- \label{fig:midlands2005_2010Degree}
-\end{figure}
-
\begin{sidewaysfigure}
\subsection{East Midlands network (2005-2010)}
\centering