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Roles in graphs

2019-11-22 21:56:53 作者：互联网

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?

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 $\epsilon (v)$ of a vertex $v$ is the greatest distance between $v$ and any other vertex; in symbols that is d(v,u)} $\epsilon (v)=\max _{u\in V}d(v,u)$ .

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

The diameter $d$ 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.

标签：diameter,Roles,graph,vertex,graphs,nodes,any
来源： https://www.cnblogs.com/dulun/p/11914346.html