SOCn5010 Analýza sociálních sítí
Přednáška 11: Bi-modální sítě a ekvivalence


Dualita osob a skupin (Breiger)
•Uvažujme množinu jedinců a množinu skupin tak, že hodnota vazby mezi libovolnými dvěma jedinci je
definována jako počet skupin, jichž jsou oba členy
•Hodnota vazby mezi dvěma skupinami je definována naopak jako počet osob, které patří do obou
skupin

Dualita osob a skupin (Breiger)



Dualita osob a skupin (Breiger)



Dualita osob a skupin (Breiger)



Idea of equivalence
•Concept of social roles & positions
•Similar attitudes, behaviour, etc.
•social role is determined over a number of different relations (criminal – victim, criminal –
police, etc.)
•Different types of equivalence – less ad more relaxed
•Structural vs. Automorphic vs. Regular equivalence

Structural equivalence
•„Two actors are structurally equivalent if they send ties to the same third parties, and receive
ties from the same third parties“
•They do not need to have a direct tie to each other to be equivalent
•Similarity: similar social environments provoke similar responses
•Directed, undirected and self-loops network data
•Grouping of structurally similar data: blockmodel
•
•

Structural equivalence
•Profile similarity
•Direct method - optimatization

Automorphic equivalence
•identifies actors that have the same position, or who are completely substitutable
•sets of actors can be equivalent by being embedded in local structures that have the same patterns
of ties -- "parallel" structures
•If exchanged - all of the distances among all the actors in the graph would be exactly identical

Regular equivalence
•the same profile of ties with members of other sets of actors that are also regularly equivalent
•actors can be structurally similar in ways that do not involve being connected to the same actors
•similar patterns:
•structural equivalence - two teachers are structurally equivalent if they teach the same students
•regular equivalence - teachers have to teach at least one student each

Core - periphery
•partition of the nodes into two groups: the core and the periphery
•The core block contains the core-to-core interactions, and the peripheral block contains the
periphery-to-periphery interactions, with the two off-diagonal blocks containing the
core-to-periphery and the periphery-to-core interactions
•In a core–periphery structure, we expect core nodes to be well connected to other core nodes +
peripheral nodes not to be connected to other peripheral nodes
•ideal structure the core block would be a 1-block and the peripheral block would be a 0-block
•cannot be directly applied to valued data

Literatura
•SIMMEL, Georg. 1964. „The Web of Group-Affiliations.“ Pp. 127-185 in Conflict and The Web of
Group-Affiliations. New York: The Free Press.
•BREIGER, Ronald. 1974. “The Duality of Persons and Groups,” Social Forces 53: 181-190.
•CROSSLEY, Nick. 2010. Towards Relational Sociology. Abingdon: Routledge.
•PRELL, Christine. 2012. Social Network Analysis: History, Theory & Methodology. Los Angeles: Sage.
•KNOKE, David, and Song YANG. 2008. Social network analysis. Thousand Oaks: Sage.
•