# toryrailu'alujvo

x1 is the geodesic path from x2 to x3 via or through points including/on connected manifold component/in connected graph component x4, with distance being measured by standard/metric/weighting x5.

x1 and x2 must belong to the same connected component (which includes/encompasses x4). The overall 'distance' travelled must be the minimal option under the orientation (from x2 to x3; this is not always symmetric) and path weighting/the specified metric such that the points x4 are included in the path or the path is in/on connected manifold/graph component x4 (as appropriate). In other words, x1 includes a geodesic from x2 to x3 through/on/along/in points or space x4. If the notion of distance is well-formed, then the triangle inequality should be satisfied and, therefore, x1 should be composed of certain of geodesic subpaths between points in x4 U Set(x2, x3). If x4 is oriented or is an ordered list of points, then the path must connect them in that order (or a permitted order if there are multiple options).

## In notes:

grafyjbi
x1 (node in graph) is near x2 (node in same connected graph component), such that they are path-connected, along path(s) x3 (default: at least one pairwise graph geodesic, with no restriction on which paths are considered) according to edge weighings x4 in connected graph component x5, with nearness standard/satisfying other conditions x6.
grafyjbirai
x1 (node in graph) is among the very nearest nodes to x2 (node in same graph), such that they are path-connected, along path(s) or paths of type x3 (default: directed graph geodesics from x2 to candidate other nodes, such that each of these candidates (plus x1) are pairwise distinct from x2) according to edge weighings x4 in connected graph component x5, with nearness standard/satisfying other conditions x6, the extreme x7 (default: ka zmadu, implying most-near) being amongst set/range x8 of candidate nodes.
utka'au
x1 and x2 are path-linked by binary predicate x3 (ka; possibly non-symmetric/non-commutative) via a from-x1-to-x2-directed graph geodesic of length x4 (li; nonnegative integer or positive infinity) in graph x5 (default: maximal) which is generated by relation x3.