Eccentricity, radius and diameter are terms that are used often in graph theory. They are related to the concept of the distance between vertices. The distance between a pair of vertices is the length of a shortest path between them. We begin by reviewing some of the properties of distance in graphs. Then we define the eccentricity of a vertex (which is the maximum distance from it to any other vertex in the graph), the diameter of a graph (the maximum eccentricity) and the radius of a graph (the minimum eccentricity). We use two examples to illustrate these concepts. Furthermore, the periphery and centre of a graph are the set of vertices whose eccentricity is the diameter and radius, respectively. Notice that the examples used in the video are very small and so the vertices are either in the periphery or centre, but notice that in general there may be many vertices which lie in neither the periphery or the centre. -- Bits of Graph Theory by Dr. Sarada Herke.
Related videos:
- Graph Theory: 05. Connected and Regular Graphs
- Graph Theory: 50. Maximum vs Maximal
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