复杂网络基础知识--图的各种距离定义
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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
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