Network Roles

Social networks tend to have people that fill positions within the community. For example, within an academic community the roles of being a professor or a student can sometimes be identified solely by using the directed interactions among the individuals. To perform such an analysis, some measure of equivalence is used. In Social Network Analysis by Wasserman and Fauts, the following definitions of equivalence are reviewed (each with a note):

1. Structural Equivalence - requires identical ties to other identical actors
   
2. Automorphic and Isomorphic Equivalence - requires identical ties to other actors
   
3. Regular Equivalence - actors have identical ties to and from equivalent actors
   
4. Local Role Equivalence - actors are role equivalent if they have the same role sets
   
5. Ego Algebra Equivalence - based on algebra of relational structuresSo, why is knowing how to use this important? Well, say you would like to better understand the network surrounding your blog by learning which other blogs are similar in their ties as you, then this is how you could do it.