Roles in graphs

related website: Beyond Community Detection - RolX; ReFeX and RolX ;

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; bridges between groups; central connectors.

Why are roles important?

roles of individual nodes can also be gleaned收集的 from the structure of the graph. Combined with community detection, role detection can add crucial insight when looking for key information such as:

• Who are the most important, most connected figures - the “key influencers”?
• Which members are highly connected to multiple close-knit communities, forming “bridges” in the network?
• What distinguishes communities with almost no connections to the rest of the graph, from communities deeply embedded inside it?

The analysis required to answer these questions is complementary to community detection

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.