MelNet

General

Dependence assumption: Theoretical assumption about dependencies among possible network ties; determines the type of parameters in the model.
Exponential random graph models: a model for a social network, expressing a probability distribution of graphs with an exponential form: see also p*.
Homogeneity assumption: Assumption about which parameters to equate, to make the model identifiable (see Koskinen et al., 2018).
Graph statistics: for homogeneous models these are counts of the configurations in the observed graph; more generally they may depend also on node-wise or dyad-wise covariates
Network Configuration: A small sub-graph that may be observed in the data and that is represented by parameters in the model: eg reciprocated ties, triangles.
Parameters: relate to specific network configurations that may be observed in the graph; a large positive parameter is interpreted as the presence of more of the configurations than might be expected from
chance (given the other effects in the model); a large negative parameter signifies the relative absence of the configuration.
p*: the term for exponential random graph models introduced by Wasserman and Pattison (1996).

Edge and dyad independence models:

Dyad independence: assumes that dyads are independent of one another; the model includes edge and
reciprocity parameters, and possibly also node or dyad attributes.
p1 models (Holland and Leinhardt): an early dyad independence model, including popularity and expansiveness effects.
p2 model: elaboration of p1 model, where popularity and expansiveness effects are random, and independent variables may be used to predict ties.
Simple random graphs, Bernoulli graphs, Erdos-Renyi graphs: assume that edges are independent of one another and are observed with a given probability.

Markov random graph models

alternating k-stars: a Markov parameter (and statistic) but used in the new higher order models; a particular combination of Markov k-star counts into the one statistic; equivalent to geometrically weighted degree counts; useful for modelling the degree distribution.
cyclic triad: a Markov graph configuration: in a directed network, ties ij, jk and ki are observed among actors i, j, and k.
degeneracy (or near-degeneracy): when a model implies that very few distinct graphs are probable, often only empty or complete graphs; degenerate models cannot be good models for social network data.
geometrically weighted degree counts: a statistic (and parameter) in higher order models: a sum of degree counts with geometrically decreasing weights; equivalent to alternating k-stars.
k-star: a Markov graph configuration: in a non-directed graph, k edges are expressed by the one actor.
k-in-star: a Markov graph configuration: in a directed graph, k arcs are directed to the one actor.
k-out-star: a Markov graph configuration: in a directed graph, k arcs are expressed by the one actor.
Markov dependence assumption: introduced by Frank and Strauss (1986), proposes that, conditional on the rest of the graph, two possible ties are dependent on one another when they share an actor.
mixed-star: a Markov graph configuration: a two path in a directed graph.
transitive triad: a Markov graph configuration: in a directed network, ties ij, jk and ik are observed among actors i, j, and k.
triangle: a Markov graph configuration: in a non-directed network, a clique of three actors, ties ij, jk and ik are observed among actors i, j, and k.