All of our network analysis was conducted with a software package called Graph Tool \cite{peixoto_graph-tool_2014}

Evaluated Networks

Artifical Networks

The artificial networks we evaluated were 5 layer fully connected ANNs. The network was trained on the task of converting a binary value of length 10 to a decimal value \citep{liang2016deep}. For example, \(1010101001\) to \(681\). We chose ANNs as our example of an artifical network over something like an organizational hierarchy because ANNs can be designed very precisely, have very clear performance metrics  and are quick to develop. 
Three networks of this class were created with a constant set of nodes: Narrow, Constant, and Wide. Each network has the same amount of input (\(10\)) and output nodes (\(1\)). The differences in the network were the number of nodes in each hidden layer and as a result the number of edges in each graph. The Narrow Net (as shown in Figure \ref{222154})  starts wide in the first hidden layer with \(25\) nodes and progressively gets narrower by five nodes per layer for four layers (\(10\ \rightarrow\ 25\ \rightarrow\ 20\ \rightarrow\ 15\ \rightarrow\ 10\ \rightarrow\ 1\))