New Graphlet Orbit Covariance Term for the 'ergm' Package – introduced under 'ergm.graphlets' package


This is a new term for the ergm package that links the graphlet structures in the network for a given graphlet orbit with numeric node attributes.


The function ergm is used to fit linear exponential random graph models, in which the probability of a given network, y, on a set of nodes is \exp{θ * g(y)}/c(θ), where g(y) is a vector of network statistics for y, θ is a parameter vector of the same length and c(θ) is the normalizing constant for the distribution.

The network statistics g(y) are entered as terms in the function call to ergm. The ergm package contains a wide range of terms. For the details on the possible <model terms>, see ergm-terms.

The ergm.userterms package provides a template for adding new terms. The terms can be used throughout the ergm package and behave identically to the supplied terms.

The Graphlet Orbit Covariance Term

grorbitCov(attrName, grOrbit)

The correlation between a node's graphlet degree and a numeric attribute value can be included into an ERGM by using the grorbitCov term. The question that the change score function of this term answers is: what is the change in covariance between a vector of nodal attributes and nodal orbit degrees when an edge is changed? This term has two arguments: attrname and grorbit. The attrname is a character vector giving the name of a numeric attribute in the network's vertex attribute list. The optional grorbit argument is a vector of distinct integers representing the list of graphlet orbits to include into the ERGM model. When grorbit is not provided, all graphlet orbits are evaluated by default. The term adds one network statistic to the model for each element in grorbit. This term is defined for the 73 orbits corresponding to graphlets with up to 5 nodes. Therefore, grorbit accepts values between 0 and 72. Values outside this range are ignored. This term can only be used with undirected networks.


Yaveroglu ON, Fitzhugh SM, Kurant M, Markopoulou A, Butts CT, Przulj N (2015). ergm.graphlets: A Package for ERG Modeling Based on Graphlet Properties, Journal of Statistical Software 65(12), 1-29, URL

See Also

statnet, network, ergm, ergm-terms

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