Future Work

We think there is a lot of potential for future work in this direction. First of all evaluating more networks specifically ANNs where every network is ensured that it has at least the capacity of a performant network at each hidden layer, but in general more collaborative networks is important to confirm the result. It would be nice to see if there are cases where the betweeness and PageRank centrality metrics disagree to determine what actually matters in the network, the flow or the number and "quality" of connections. We would also like to evaluate more complicated and more varied networks like the nature of skip connections in layered systems or investigating ideas like churn in collaborative networks (i.e. dropout, job change etc.). There are organizational hierarchy datasets out there like those assembled by the US Government, however a suitable performance metric should be determined for these networks before analyzing them. The main variable we altered in our artificial networks, the width of hidden layers had a large impact on the number of edges in the network, so analyzing constant edge networks would be interesting. There are other metrics to measure like cohesion indices \cite{belau2014consequences} and the fractal scaling found in self organizing networks \cite{laurienti2011universal} and it would be interesting to compare the qualitative findings of this study with the measure of algebraic topological capacity shown in Guss et al. \cite{guss2018characterizing} We would also be interested in looking at developing or applying a notion of role centrality to analyzing these networks. There also interesting applications of this work, including identifying nodes susceptible to adversarial attacks and designing mitigation factors, intelligent dropout for the training of neural networks in addition to applying the lessons learned to collaborative network design.