  A geodesic is the shortest path between two vertices in a connected network.
The geodesic is the kernel of various network metrics including radius,
diameter, eccentricity, closeness, and betweenness. These metrics are the
foundation of much network research and thus, have been studied extensively in
the domain of single-relational networks (both in their directed and undirected
forms). However, geodesics for single-relational networks do not translate
directly to multi-relational, or semantic networks, where vertices are
connected to one another by any number of edge labels. Here, a more
sophisticated method for calculating a geodesic is necessary. This article
presents a technique for calculating geodesics in semantic networks with a
focus on semantic networks represented according to the Resource Description
Framework (RDF). In this framework, a discrete "walker" utilizes an abstract
path description called a grammar to determine which paths to include in its
geodesic calculation. The grammar-based model forms a general framework for
studying geodesic metrics in semantic networks.
