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What does geodesic distance mean?
A simple measure of the distance between two vertices in a graph is the shortest path between the vertices. Formally, the geodesic distance between two vertices is the length in terms of the number of edges of the shortest path between the vertices.
What is meant by geodesic in mechanics?
In the original sense, a geodesic was the shortest route between two points on the Earth’s surface. More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it.
What is distance in a graph?
The distance between two vertices and of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path exists (i.e., if the vertices lie in different connected components), then the distance is set equal to. .
How is the geodesic distance between two vertices defined?
Formally, the geodesic distance between two vertices is the length in terms of the number of edges of the shortest path between the vertices. For two vertices that are not connected in a graph, the geodesic distance is defined as infinite. Using geodesic distance, we can define several other useful measurements for graph analysis and clustering.
Which is a property of a geodesic path?
Geodesic paths are not necessarily unique, but the geodesic distance is well-defined since all geodesic paths have the same length. One large-scale property of networks is the average geodesic distance between pairs of nodes in the network. One of the most discussed network phenomena is the small-world effect.
Are there any geodesics that are locally distance minimizing?
In Riemannian geometry, all geodesics are locally distance-minimizing paths, but the converse is not true. In fact, only paths that are both locally distance minimizing and parameterized proportionately to arc-length are geodesics.
Where does the word’geodesic’come from in geography?
The noun “geodesic” and the adjective “geodetic” come from geodesy, the science of measuring the size and shape of Earth, while many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth’s surface.