~williamvds/dissertation

0413ca30d608d51989f68f66be200a755ccb791a — williamvds 4 years ago aa736b5
Move network analysis graphs into main body
1 files changed, 43 insertions(+), 43 deletions(-)

M dissertation.md
M dissertation.md => dissertation.md +43 -43
@@ 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