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

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Description

This is a new term for the ergm package that counts the number of graphlets in the network for a given graphlet type.

Details

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 Count Term

graphletCount(g)

Statistics for the number of times that a graphlet appears in a network can be included in an ERGM by using the graphletCount term. The question that the change score function of this term answers is: how do the number of graphlets of type G_i change when an edge is flipped in the network? This term has an optional argument, g. g is a vector of distinct integers representing the list of graphlets to be evaluated during the estimation of model coefficients. When this argument is not provided, all graphlets are evaluated by default. The term adds one network statistic to the model for each element in g. This term is defined for the 30 graphlets with up to 5 nodes. Therefore, g accepts values between 0 and 29. Values outside this range are ignored.

References

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 http://www.jstatsoft.org/v65/i12/.

See Also

statnet, network, ergm, ergm-terms