Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere. The word "diameter" is derived from Greek διάμετρος (diametros), "diameter of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "measure". It is often abbreviated DIA, dia, d, or ⌀.

In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter (which refers to the line itself), because all diameters of a circle or sphere have the same length, this being twice the radius r.

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

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. 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 between two vertices and is defined as the length of a shortest path from to consisting of arcs, provided at least one such path exists. Notice that, in contrast with the case of undirected graphs, does not necessarily coincide with , and it might be the case that one is defined while the other is not.

Related concepts

A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected.

Diameter (protocol)

Diameter is an authentication, authorization, and accounting protocol for computer networks. It evolved from and replaces the much less capable RADIUS protocol that preceded it.

Diameter Applications extend the base protocol by adding new commands and/or attributes, such as those for use with the Extensible Authentication Protocol (EAP).

Comparison with RADIUS

The name is a play on words, derived from the RADIUS protocol, which is the predecessor (a diameter is twice the radius). Diameter is not directly backwards compatible but provides an upgrade path for RADIUS. The main features provided by Diameter but lacking in RADIUS are:

Applications

A Diameter Application is not a software application but is a protocol based on the Diameter base protocol defined in RFC 6733 (Obsoletes: RFC 3588). Each application is defined by an application identifier and can add new command codes and/or new mandatory AVPs (Attribute-Value Pair). Adding a new optional AVP does not require a new application.