Many of the interesting networks in the world are collaborative networks, where nodes work together to accomplish larger tasks than any one can complete by themselves. These networks describe how we build things, how bees survive the winter, how computers analyzes terabytes of data and how we and computers can perceive the world. However, designing these networks is difficult unless the task itself can be described concretely. For instance structuring a corporation to maximize profit may result in applying the current management trends then refining based on returns.
In this work we want to explore the potential for topological metrics that network designers can apply in designing their systems. The metrics we chose to evaluate were betweenness centrality, PageRank centrality, in/out degree distribution and all pairs max flow. We use these metrics to evaluate networks of various effectiveness from the realms of artificial neural networks, naturally occurring networks and randomly generated ones.
We find that low variance in betweeness centrality and low mode and mean of PageRank are signs of effective networks and we see that there is a natural tendency for the flow of collaborative networks to narrow from source to sink instead of the flow spreading to use excess capacity later in the path. This leads us to support a common held intuition for feedforward neural network design, which is to determine the necessary capacity of the final hidden layer and make the preceding networks progressively wider. We believe that centrality is an important quality of effective networks and see this work as evidence that further work in this direction is a good idea.