1. HCC class lecture 23 comments John Canny 4/18/05

2. Administrivia Reminder: Project presentations on May 9 and 11.

3. Role and Position Role is an intuitive idea: it is what the actor “does” in the network. People with similar roles should be interchangeable in the network, so role analysis is similar to paradigmatic analysis from semiotics.

4. Role and Position Position is an explicit set of similar actors. These actors share the same set of relations with others. Role is the pattern of relations between the actors. Therefore role is the more abstract, portable notion. E.g. Mother, child, manager, travel agent, can be defined by particular sets of relations between these actors and certain other. The position of father in a particular network is the set of actors who act as fathers to others in the network.

5. Equivalence Regular equivalence: Regular equivalence: Actors are equivalent if they have ties to others with the corresponding roles. e.g. A has the role of mother because of ties to B, C, D, who have the role of “son” or “daughter”.

6. Equivalence Regular equivalence: Regular equivalence: Actors are equivalent if they have ties to others with the corresponding roles. e.g. A has the role of mother because of ties to B, C, D, who have the role of “son” or “daughter”.

7. Equivalence Structural equivalence is an easy notion to deal with, since it depends on the actual identities of the neighbors. E.g. correlations or euclidean distance comparison can be used. Regular equivalence is a more useful idea, but is trickier because its definition is recursive: One must know the neighbors roles’ before assigning a new role. Regular equivalence is an active area of research, although some solutions exist.

8. Hierarchical clustering One natural way to build a regular equivalence relation is to hierarchically cluster the data: Actors are clustered together if they have the similar relations to other actors (structural equivalence). Then we repeat the clustering on the abstracted graph (actors are clusters from the previous step), etc… In this way, neighbors are labeled with “roles” from the previous step.

9. Discussion Topics T1: How do role and position relate to communities of practice? Are such communities actually “positions” in a network, or do they have internal roles, or both? T2: The readings argue that its often helpful to use “typed” ties (e.g. a tie that is explicitly labeled “mother”). By using example networks that you know, critique this idea. Can ties always be typed? Or are there ties whose type may not be known a priori?