Role-equivalent Actors in Networks ? Group Structures Beyond Dense Communities

Communities in social networks are often defined as groups of densely connected actors. However, members of the same dense group are not equal but may differ largely in their social position or in the role they play. Furthermore, the same positions can be found across the borders of dense communities so that networks contain a significant group structure which does not coincide with the structure of dense groups. This papers gives a survey over formalizations of network-positions with a special emphasis on the use of algebraic notions.