In Visualizing Social Networks, I found that the Minimum Spanning Tree (MST) is a scalable way to visualize large social networks. But it has some problems…
Meet a close cousin of MST, the balanced, degree-constrained Arborescence. A single overall leader is chosen using the Harmonic Centrality algorithm, unlike MST which is more decentralized. The MST is too “flat”, so a limit was placed on the number of direct connections that each person can have (degree-constrained). This provides more opportunities for advancement within the ranks. It is easier to level-up. The algorithm is balanced, so that all leaders at the same rank lead organizations of comparable size. These changes are designed to match people’s expectations of what a just-for-fun corporate/military hierarchy should look like.
The code is on Github.