Table 2.

Hierarchy structure measures associated with each matrix dataset in the archive.

measure (column name in metadata)	range	description	dataset criteria	source
directional consistency index (dci)	0–1	the average directional asymmetry in wins across dyads. 1 = all dyads have one individual who wins every interaction, 0 = all dyads are ties.	matrix_edgelist = ‘matrix’ countbinary = count	[145]
triangle transitivity index (ttri)	mostly 0–1, rarely <0	the proportion of triads in the network of dominance relationships that are transitive, scaled so that 0 = expected triangle transitivity under random interactions and 1 = perfectly transitive. Rarely, negative values can occur if dominance relationships are less transitive than expected under random interactions.	matrix_edgelist = ‘matrix’	[206]
modified Landau's h’ measure of linearity (modified_landaus_h)	0–1	a measure of the linearity of dominance relationships, or the degree to which dominance relationships show transitive properties. 0 = completely cyclical hierarchy, 1 = completely linear hierarchy. This value is biased downward with increasing proportions of unknown relationships [225]; triangle transitivity is recommended as an alternative measure [206].	matrix_edgelist = ‘matrix’ countbinary = count	[226]
hierarchy steepness (ds_steepness)	0–1	a measure of the differentiation in winning ability among individuals, calculated as the absolute value of the slope of a line fitted through the normalized David's Scores of all contestants. David's Scores measure an individual's winning tendency.	matrix_edgelist = ‘matrix’countbinary = count	[110]
		0 = all individuals have the same score, 1 = all individuals are maximally differentiated in their scores. This value is biased downward with increasing proportions of unknown relationships [225].