Definition by analogy for "not hierarchical"

Question (fill in the blank): Vertical is to hierarchical as horizontal is to _______?

Google searching for this word using synonym, antonym, and 'orthogonal to' haven't given me what I'm looking for. Equal is inappropriate, and I'd like to avoid phrases like "equal rank." Furthermore, "peer" has a social connotation I'd like to avoid. So essentially: independent but of the same hierarchical rank/stratum... "equistratic"?

I'm leaning toward "contemporaneous" but I'm hoping for a word that has a static connotation rather than dynamic/transient. I may also go with "commensurate" from Word for having the same rank.

Linear seems to be correct.

When linearity prevails over hierarchy in syntax

[Proceedings of the National Academy of Sciences of the USA.]

PNAS

In the context of organizational structure, a hierarchical structure stresses vertical accountability whereas a flat structure stresses (horizontal) egalitarianism.

A flat organization refers to an organization structure with few or no levels of management between management and staff level employees. The flat organization supervises employees less while promoting their increased involvement in the decision-making process. - Colette L. Meehan, Flat Vs. Hierarchical Organizational Structure

In this context,

• Vertical is to hierarchical as horizontal is to flat.