Target node x1 and primary subject node x4 belong to the same (single) strictly-directed, connected tree graph/network/hierarchy or are related by relation scheme x5 such that x1 has coordinates (x2, x and x4 has coordinates (0, 0) according to the labelling scheme which is described in the notes hereof.
This word makes all basic familial relationships easily expressible and regular. x2 is a nonnegative integer; x3 is an integer (potentially of any signum a priori). x5 is directed and thus admits descriptions such as "rootward", "parent", "superior"/"ancestor", "leafward", "child", and "descendant"/"subordinate". x4 is a node which is identified and singled out as being special in the tree, and thus the relationship is not entirely symmetric under exchange of x4 with any other node. For any target node v in x5, the coördinate label for v is determined as follows: For the sake of ease and uniformity of notation, denote x4 by "μ"; likewise denote x5 by "G". Let/require/assume that the most-recent common direct ancestor of μ and v in/according to G be essentially-unique and denoted by "mrcdaG(μ, v)"; let δ be the Kronecker delta function on the nodes of G; let ρ be a binary function on the Cartesian square of the set of nodes of G mapped to the nonnegative intergers or positive infinity, and be the undirected graph-geodesic distance between its inputs. Let the coördinate label assigned to v be coördG, μ(v) = (ξG, μ(v), υ= (ξ, υ) = ((1 - δ(v, mrcdaG(μ, v))) ρ(μ, mrcdaG(μ, v)), ρ(v, mrcdaG(μ, v)) - ρ(μ, mrcdaG(μ, v))). Under these conditions, unique relations/path-shapes which connect μ to v are bijective with the labels; under these conditions, the mapping from labels to nodes should be injective. For example: Assume that x4 is oneself for simplicity and that x5 is one's family tree under the assumption that it records only human genetic relationships due to binary sexual reproduction/inheritance and excludes incest (regardless of the graph-geodesic distance otherwise between the participants), marriage or similar relationships, co-parenting, in-law relationships, half or other partial family relationships, step-familial relationships, adoptions, cross-generational co-parenting, distinctions according to age alone or comparisons thereof, and distinctions according to gender/sex alone or comparisons thereof. In this case, if oneself is labelled by (0, 0), then: one's children are labelled by (0, 1), one's grandchildren are labelled by (0, 2), one's nth-great-grandchildren are labelled by (0, 2+n), one's parents are labelled by (0, -1), one's grandparents are labelled by (0, -2), one's nth-great-grandparents are labelled by (0, -(2 + n)), one's siblings are labelled by (1, 0), one's niblings (children of siblings) are labelled by (1, 1), one's nibling's children are labelled (1, 2), one's neams (siblings of parents) are labelled by (2, -1), one's 1st cousins 0 times removed (children of neams) are labelled by (2, 0), one's first cousins once removed via neams are labelled by (2, 1), etc. Notice that corporate organization charts, as directed from CEO (root) toward subordinates, can have similar labels. See also: "tamne", ".anseingu", "grafnseljimcnkipliiu".