<abstract xmlns="http://www.w3.org/1999/xhtml"><p>An affiliation network consists of actors and events. Actors are affiliated with each other by virtue of the events they mutually attend. This article introduces a family of affiliation measures that captures the extent of actors’ affiliations in the network. At one extreme, one might have an actor who attended many events, but none of these events were attended by any of the other actors in the network. Although of high degree, in no reasonable interpretation would such an actor be considered highly affiliated with other actors in the network. At the other extreme, one might have an actor defined by a collection of events, all of which were attended by another actor(s), making the actor as enmeshed in the network as possible. Most actors will be between these extremes, with some events being shared by varying others, and some not. This article introduces a family of affiliation measures based on the entries of the co-occurrence matrix. After defining the measures, the cumulative distribution function of first-order affiliation is derived and expressed as a difference of binomials.</p></abstract>

An affiliation network consists of actors and events. Actors are affiliated with each other by virtue of the events they mutually attend. This article introduces a family of affiliation measures that captures the extent of actors’ affiliations in the network. At one extreme, one might have an actor who attended many events, but none of these events were attended by any of the other actors in the network. Although of high degree, in no reasonable interpretation would such an actor be considered highly affiliated with other actors in the network. At the other extreme, one might have an actor defined by a collection of events, all of which were attended by another actor(s), making the actor as enmeshed in the network as possible. Most actors will be between these extremes, with some events being shared by varying others, and some not. This article introduces a family of affiliation measures based on the entries of the co-occurrence matrix. After defining the measures, the cumulative distribution function of first-order affiliation is derived and expressed as a difference of binomials.

A Family of Affiliation Indices for Two-Mode Networks<sup>*</sup>

Journal of Social Structure

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Family of Affiliation Indices for Two-Mode Networks

{"article-title":{"content":"A Family of Affiliation Indices for Two-Mode Networks","sup":"*"}}

An affiliation network consists of actors and events. Actors are affiliated with each other by virtue of the events they mutually attend. This article...

A Family of Affiliation Indices for Two-Mode Networks^*

Published Online: Aug 14, 2019

Page range: 1 - 19

DOI: https://doi.org/10.21307/joss-2019-024

Keywords
Affiliation networks, network methodology, statistical methods, two-mode networks

© 2019 Frank Tutzauer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Family of Affiliation Indices for Two-Mode Networks*

Published Online: Aug 14, 2019

Page range: 1 - 19

DOI: https://doi.org/10.21307/joss-2019-024

KeywordsAffiliation networks, network methodology, statistical methods, two-mode networks

© 2019 Frank Tutzauer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Family of Affiliation Indices for Two-Mode Networks^*

Keywords
Affiliation networks, network methodology, statistical methods, two-mode networks