x1 (node in a tree graph) and x2 (node in the same tree graph) have an essentially unique most recent (graph-nearest) common ancestor node A such that x3 [nonnegative integer; li] is the minimum element of the set consisting only of d(A, x1) and of d(A, x2), and such that x4 [integer; li] is d(A, x1) - d(A, x2), where d is the graph geodesic distance (defined to be infinite if nodes are not connected in the correct direction).
While technically not good, this definition also employs the convention that x3 is positive (countable) infinity if A does not exist, meaning that x1 and x2 belong to mutually disjoint trees (or if at least one of them is undefined); in this case, x4 is not well-defined (see: "zi'au"). This word can be used to specify the concept of "nth cousin m-times removed"-ness; x1 and x2 would be the cousins, x3-1 = n, and x4 is closely related to m but is signed. If one views the tree graphs to which x1 and x2 belong with the viewing perspective such that siblings and spouses are mutually separated horizontally and such that ancestors are separated from their descendants vertically, then x3 is the unsigned horizontal distance between x1 and x2. x4 is, approximately, the signed generational offset/difference between subjects x1 and x2; it it their signed 'vertical' difference under the aforementioned viewing perspective. The relationship need not actually be cousinhood (as perceived by English); direct ancestor-descendant pairs, (aunt/uncle)-(niece/nephew) pairs, and in fact any pair of family members with a well-specified most recent common ancestor (that is known) have this relationship to one another. This word can be used for specifying the number of "great"'s in the title of a relationship between x1 and x2 (with some calculational forethought). The tree diagram can be more generic than a family tree though; thus cousinhood is just a way to put it into context/application and is not really essential to the meaning except through analogy. Notice the ordering of all terms; if the graph is directed, the arguments of the distance matters. The graph should probably be a tree locally if it is to be a well-defined relationship. x3 is unchanged but x4 is negated (multiplied by -1) by/under exchange of x1 and x2. The ordered pair (x3, x is named "consanguistance between x1 and x2 (in that order)" by Curtis Franks. For a normal family tree and fixed x1 therein, consanguistance produces countably many equivalence classes of nodes. It does not recognize the difference between half or full relatives, marriages/parentings are either unsupported (when x3 > 0) or are reduced to be equivalent (when x3 = 0 and x4 \neq 0), and gender/sex are ignored/reduced to equivalence. The set of nodes x2 with x3 = 0 is called x1's (the subject's) genealogical line (id est: if x3 = 0, then x1 re'au'e ja se dzena x2 according to the edge relation on the graph or x1 = x2); the set of nodes with x3 > 0 are sibling/branch/side lines, which could be labelled and ordered, but doing so would be somewhat difficult with this word. This word focuses on the relationship between x1 and x2, not the relationship between each of them and A; for that, see anseingu. The underlying tree graph is, modulo an equivalence relation involving tseingu, a 'quipyew' tree graph (see "grafnkipliiu").