Conclusion

In this work we set out to find a set of topological metrics that could help inform network designers on ways to construct their collaborative networks. We identified betweenness centrality, and PageRank centrality as two measures worth looking at. In addition we also mapped the distribution of the in and out degrees of the networks we analyzed and we also determined the all pairs max flow of the networks. 
In doing so we saw that centrality is a metric which differentiates effective networks from less effective ones, where networks with low variance for betweenness centrality, and low mean and mode for PageRank do better. This leads us to believe that centrality is important in the effectiveness of these networks and that highly bottlenecked networks are not as effective as networks which are slightly less bottlenecked. We saw evidence to support the findings of Radford et al. and Guimar et al. that there are nodes that do much of the work and others that serve to nudge the result slightly.  We also saw that these networks have a tendency to narrow flow as they move further from the source, explaining why the varience and mode and mean for betweennes centrality and PageRank centrality respectively are higher in less performant networks. Because of this flow result some of the intuition commonly applied to network design, that being of start wide and narrow/condense decision making is supported. Therefore we recommend with designing at least feed-forward networks to start by determining the necessary capacity for the output layer then making each preceding layer progressively wider. We think that this work may signal that there is potential to add formalism to collaborative network design.