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 of a vertex
is the greatest distance between
and any other vertex; in symbols that is d(v,u)}
.
The radius of a graph is the minimum eccentricity of any vertex.
The diameter 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.