Summary: Stationary point processes in \(\mathbb{R}^{2}\) with two different types of points, say \(H\) and \(L\), are considered where the points are located on the edge set \(G\) of a random geometric graph, which is assumed to be stationary and connected. Examples include the classical Poisson-Voronoi tessellation with bounded and convex cells, aggregate Voronoi tessellations induced by two (or more) independent Poisson processes whose cells can be nonconvex, and so-called \({\beta}\)-skeletons being subgraphs of Poisson-Delaunay triangulations. The length of the shortest path along \(G\) from a point of type \(H\) to its closest neighbor of type \(L\) is investigated. Two different meanings of “closeness” are considered: either with respect to the Euclidean distance (e-closeness) or in a graph-theoretic sense, i.e., along the edges of \(G\) (g-closeness). For both scenarios, comparability and monotonicity properties of the corresponding typical shortest-path lengths \(C^{e\ast}\) and \(C^{g\ast}\) are analyzed. Furthermore, extending the results which have recently been derived for \(C^{e\ast}\), we show that the distribution of \(C^{g\ast}\) converges to simple parametric limit distributions if the edge set \(G\) becomes unboundedly sparse or dense, i.e., a scaling factor \({\kappa}\) converges to zero and infinity, respectively.