András Vörös
Department of Social Statistics, University of Manchester
SOST71032 Social Network AnalysisAssignment
Introduction to Exponential Random Graph Models (ERGMs)
The intuition
(Thanks to Bálint Néray and Zsófia Boda for some of the content on these slides!)
 What are ERGMs and what are they good for?
 Theories and mechanisms of social network formation
 ERGM assumptions and inference to social processes
 Typically modeled network configurations
 An example
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Outline
 “Exponential random graph models (ERGMs) are statistical models for network
structure, permitting inferences about how network ties are patterned.”
(Lusher, Koskinen & Robins 2013, Chapter 2)
 Goal:
 to understand an observed network structure (nb: not to predict single network ties!)
 to find underlying processes creating and maintaining the network-based social system
 Tie-based approach – ERGMs do not model individual outcomes
(though see extensions)
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What are ERGMs?
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The rationale behind ERGMs
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The rationale behind ERGMs
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The rationale behind ERGMs
Network ties can be explained…
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The rationale behind ERGMs
Network ties can be explained…
… with attributes of the sender and receiver nodes…
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The rationale behind ERGMs
Network ties can be explained…
… with attributes of the sender and receiver nodes…
… and with the structure of
their local network neighborhood.
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The rationale behind ERGMs
Network ties can be explained…
… with attributes of the sender and receiver nodes…
… and with the structure of
their local network neighborhood.
Flexibility regarding the “local
network neighborhood” part.
 Simplistic summary 1:
 ERGMs are statistical models that express how different (structural, individual, contextual)
factors contribute to the probability that a network tie is observed*
 Simplistic summary 2:
 ERGMs aim at assessing the effects of various network configurations surrounding a tie on the
probability of the tie being present*
 Simplistic summary 3:
 ERGMs are a kind of logistic regression where the dependent variable is the odds of a tie in
the network being present and the explanatory variables are statistics representing the
structure of the network around the tie in question*
* these apply to the basic model and are slightly different for extensions (to be discussed later)
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So, what are ERGMs?
 Interdependence between actors – networks!
 Interdependence between ties
 Dyadic
 Markov
 Social circuit
 etc.
 Standard statistical models assume independence – not suitable
 ERGMs model network ties by explicitly taking into account their
interdependences
 Flexibility – many forms of dependence can be expressed
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Why should we use ERGMs? – Interdependence!
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Please continue with the next topic