Sender- and Receiver-specific blockmodels

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Journal of Social Structure

International Network for Social Network Analysis

Subject: Social Sciences

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eISSN: 1529-1227

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VOLUME 16 , ISSUE 1 (December 2015) > List of articles

Sender- and Receiver-specific blockmodels

Zhi Geng / Krzysztof Nowicki *

Keywords : Directed graph, Blockmodeling, Out-nets, In-nets, Ego-nets, EM algorithm, Multinomial distribution

Citation Information : Journal of Social Structure. Volume 16, Issue 1, Pages 1-34, DOI: https://doi.org/10.21307/joss-2019-015

License : (CC BY-NC 4.0)

Published Online: 13-August-2019

ARTICLE

ABSTRACT

We propose a sender-specific blockmodel for network data which utilizes both the group membership and the identities of the vertices. This is accomplished by introducing the edge probabilities (θi,v) for 1 ≤ i ≤ c, 1 ≤ v ≤ n, where i specifies the group membership of a sending vertex and v specifies the identity of the receiving vertex. In addition, group membership is consider to be random, with parameters (Pi)ic=1·We present methods based on the EM algorithm for the parameter estimations and discuss the recovery of latent group memberships. A companion model, the receiver-specific blockmodel, is also introduced in which the edge probabilities (ψu,j) for 1 ≤ u ≤ n, 1 ≤ j ≤ c depend on the membership of a vertex receiving a directed edge. We apply both models to several sets of social network data.

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