grorbitDist: New Graphlet Degree Distribution term for the 'ergm' Package...

In ergm.graphlets: ERG Modeling Based on Graphlet Properties

Description

This is a new term for the ergm package that evaluates the graphlet degree distribution of a network for a given graphlet orbit.

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 Degree Distribution Term

grorbitDist(grorbit, d)

The graphlet degree distributions of various graphlet orbits can be included into the ERGM by using the grorbitDist term. The question that the change score function of this term answers is: how do the number of nodes having graphlet degree n for orbit i change when an edge is flipped? This term has two arguments: grorbit and d. The grorbit argument is a vector of distinct integers representing the list of graphlet orbits to include into the model. The d argument is a vector of distinct integers. This terms adds one network statistic to the model for each pairwise combination of the arguments in grorbit and d vectors. The statistic for the combination of (i, j) is equals to the number of nodes in the network that have graphlet degree j for orbit i. This term is defined for the 15 graphlet orbits corresponding to graphlets with up to 4 nodes. Therefore, grorbit accepts values between 0 and 14. Graphlets of size 5 are omitted for this term because of the high computational complexity of the change score computation of the term. This term is defined for undirected networks.

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

ergm.graphlets documentation built on May 29, 2017, 4:09 p.m.