The Default Hierarchy

Networks that grow by isotropic redirection — where each new node picks a random target and connects to one of that target’s neighbors — produce a peculiar structure. Most nodes become leaves, connected by a single edge. The few hubs that accumulate connections grow sublinearly with network size. No preferential attachment is built into the rule. No node is designated as more important. The hierarchy — a vast periphery of leaves around a small core of hubs — emerges from the growth mechanism alone.

Scientific teams in East Asia are disproportionately “tall” — hierarchical, with concentrated leadership — compared to teams in Western countries that are more often “large” without being tall. Analysis of 150,000 publications with author contribution statements shows this pattern persists after controlling for team size. It correlates with Hofstede’s Power Distance index and with the structure of major research funding agencies. The hierarchy isn’t imposed by a single organizational rule but reinforced by cultural norms and institutional design.

Both cases illustrate the same principle: hierarchy is the default outcome of many growth processes, and flat structures require active maintenance.

In the redirection network, the mechanism is purely local: connect to a neighbor of a random node. This innocent rule creates hierarchy because it amplifies existing structure. A node with many connections is more likely to be a neighbor of any randomly chosen target, so it accumulates more connections. Not through preferential attachment — the growth rule treats all neighbors equally — but through geometric probability. The hub is more reachable. Being more reachable makes you grow. Growing makes you more reachable.

In scientific teams, the mechanism is social and institutional. A senior researcher attracts funding. Funding supports students and postdocs. Students publish under the senior researcher’s direction. The publications attract more funding. The cycle creates hierarchical teams not because anyone intends hierarchy but because the resource flow has a natural direction: from funders to established investigators to trainees. Power Distance — the cultural acceptance of unequal power distribution — lubricates rather than creates this cycle.

The analytical insight from the redirection network is precise: the number of non-leaf nodes scales as N^μ where μ < 1. This means the fraction of nodes that are structurally important shrinks as the network grows. Hierarchy doesn’t just emerge — it intensifies. A growing network becomes proportionally more hierarchical over time because the hub-leaf ratio worsens.

Applied to research institutions: as a national research system grows (more publications, more researchers), the tall-team pattern should intensify unless actively counteracted. More papers means more junior researchers per senior investigator, which means taller hierarchies. The flat-team countries aren’t flat by default — they’re flat because specific institutional choices (collaborative funding structures, flatter academic career ladders, lower power distance norms) actively resist the hierarchical attractor.

The broader lesson: when you observe a flat structure in a growing system, you’re not observing the natural state. You’re observing successful resistance to the natural state. Flatness is maintained, not found. The redirection network never produces flat structures because nothing in its growth rule resists hierarchy. Any real system that stays flat does so because something — culture, policy, architecture — pushes against the force that hierarchy emerges from.