New Graphlet Degree Distribution term for the 'ergm' Package – introduced under 'ergm.graphlets' package
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 ergmterms
.
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
andd
. Thegrorbit
argument is a vector of distinct integers representing the list of graphlet orbits to include into the model. Thed
argument is a vector of distinct integers. This terms adds one network statistic to the model for each pairwise combination of the arguments ingrorbit
andd
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), 129, URL http://www.jstatsoft.org/v65/i12/.
See Also
statnet, network, ergm, ergmterms