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Roles in graphs

时间:2019-11-22 21:58:38      阅读:82      评论:0      收藏:0      [点我收藏+]

What are roles?

“Functions” of nodes in the network – Similar to functional roles of species in ecosystems

• Measured by structural behaviors

• Examples – centers of stars – members of cliques – peripheral nodes 

Why are roles important?

技术分享图片

Roles VS Communities:

• Roles group nodes with similar structural properties

• Communities group nodes that are wellconnected to each other

• Roles and communities are complementary 

the distance between two vertices in a graph is the number of edges in a shortest path connecting them. 

the eccentricity 技术分享图片 of a vertex 技术分享图片 is the greatest distance between 技术分享图片 and any other vertex; in symbols that is d(v,u)}技术分享图片.

The radius 技术分享图片 of a graph is the minimum eccentricity of any vertex.

The diameter 技术分享图片 of a graph is the maximum eccentricity of any vertex in the graph. 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. 

Roles in graphs

原文:https://www.cnblogs.com/dulun/p/11914346.html

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