It is a governmental structure as opposed to a hierarchical structure. Conarchy is derived from Greek words koine (common, union), and archein (head, command), and its meaning is precisely control in common, control in union.
A hierarchical structure can be represented by a pyramid, where there are many levels with a dyadic valence. Each part represents only itself when it refers to parties that are located on the upper level, while represents the totality of the system when it refers to parties that are on the lower level. A conarchical structure can be represented by a sphere formed by many points, each of which interacts with the other with respect to which it performs a function.