Description Details The Graphlet Degree Distribution Term References See Also
This is a new term for the ergm
package
that evaluates the graphlet degree distribution of a network for a given graphlet
orbit.
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.
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.
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/.
statnet, network, ergm, ergm-terms
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