Distance_(graph_theory) | TriviaQuestions.online

⭐ Core Definition: Distance (graph theory)

In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance. Notice that there may be more than one shortest path between two vertices. If there is no path connecting the two vertices, i.e., if they belong to different connected components, then conventionally the distance is defined as infinite.

In the case of a directed graph the distance $d (u, v)$ between two vertices $u$ and $v$ is defined as the length of a shortest directed path from $u$ to $v$ consisting of arcs, provided at least one such path exists. Notice that, in contrast with the case of undirected graphs, $d (u, v)$ does not necessarily coincide with $d (v, u)$ —so it is just a quasi-metric, and it might be the case that one is defined while the other is not.

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👉 Distance (graph theory) in the context of Distance

Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). The term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space.

In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance.

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⭐ Core Definition: Distance (graph theory)
👉 Distance (graph theory) in the context of Distance
Distance (graph theory) in the context of Geodesic

Distance (graph theory) in the context of Geodesic

In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line".

The noun geodesic and the adjective geodetic come from geodesy, the science of measuring the size and shape of Earth, though 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. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.

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Distance (graph theory) in the context of "Distance"

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⭐ Core Definition: Distance (graph theory)

👉 Distance (graph theory) in the context of Distance

Distance (graph theory) in the context of Geodesic