\citep{liang2016deep}. For example, $1001011011$ to $603$. Three networks of this class were created: Narrow, Constant, and Wide. The differences in the network were the counts of nodes in the hidden layers, which were as follows:
\citep{liang2016deep}

Naturally Occuring Netwroks

Two naturally occurring networks were used were an airport connection network, where directed edges show connections between airports \citep{nr}, and the weights of the edges represent the amount of traffic between the nodes. The second network is an ecology network \citep{nr}, where nodes are species in an environment, edges represent dependence of one species on another, and the weight is the amount of dependence of one species on another.

Random Networks 

Random networks were built using a Poisson random distribution that determined both the degree of each node, and the weight of each is defined as the inverse of the Euclidean distance between two nodes in a Delaunay triangulation layout. 

Metrics Used

To evaluate the networks, and note the differences the networks, a suite of metrics were used. We will go through each metric, and the reasoning for using the metric.
Betweenness:
    Betweenness allows for us to measure the bottlenecking factor of each node by measuring the number of shortest paths between two pairs of vertices 

Results

To form a baseline on how our metrics would perform, we ran the suite of metrics on 
\cite{nr}
\cite{nr}

Limitations of This Work

Conclusion

\cite{altacs2013analyzing}
\cite{dunn2006novel}
\cite{sporns2003graph}
\cite{xu2002neural}
\cite{de2014laplacian}
\cite{zhang2017network}
\cite{zhou2014object}
\cite{lettvin1959frog}
\cite{guss2018characterizing}
\cite{papo2015network}
\cite{golden1996mathematical}
\cite{michel1989qualitative}
\cite{pearson2013visualizing}
\cite{stam2007graph}
\cite{wiatowski2018mathematical}
\cite{pellionisz1987tensor}
\cite{pellionisz1988tensorial}
\cite{pellionisz1980tensorial}
\cite{pellionisz1985tensor}
\cite{grassi2010centrality}
\cite{lee2010role}
\cite{borgatti2005centrality}
\cite{breza2015network}
\cite{belau2014consequences}
\cite{del:Pozo:2011}
\cite{batool2014towards}
\cite{joyce2010new}
\cite{grassi2010centrality}

Future Work

Constant edge number, The nature of skip connections in layered systems is an interesting one,

Appendix A 

Edmonds-Karp Algorithm for Max Flow