复杂网络基础知识--图的各种距离定义

图的各种距离定义

参考自：https://en.wikipedia.org/wiki/Distance_(graph_theory)

！！欢迎补充更正

1.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

%距离：两个节点的最短路径包含的边的数目

2.The eccentricity of a vertex v is the greatest geodesic distance between v and any other vertex. It can be thought of as how far a node is from the node most distant from it in the graph.

%偏心距（可能是这么翻译）：节点v的最大距离，即所有其他节点中离得最远的节点到他它的距离

3.The radius r of a graph is the minimum eccentricity of any vertex

%半径：所有节点的偏心距中最小的值

4.The diameter d of a graph is the maximum eccentricity of any vertex in the graph. That is, d is the greatest distance between any pair of vertices or, alternatively. To find the diameter of a graph, first find the shortest path between each pair of vertices. The greatest length of any of these paths is the diameter of the graph.

%直径：所有节点中偏心距最大的值

5.A central vertex in a graph of radius r is one whose eccentricity is r—that is, a vertex that achieves the radius

%中心节点：偏心距等于半径的节点

6.A peripheral vertex in a graph of diameter d is one that is distance d from some other vertex—that is, a vertex that achieves the diameter

%边缘节点（次要节点）：偏心距等于直径的节点

7.A pseudo-peripheral vertex v has the property that for any vertex u, if v is as far away from u as possible, then u is as far away from v as possible.

%伪边缘节点：距离某节点偏心距最大的节点

附加：如果一个图中每对节点只有一条最短路径，此图为geodetic graph