Neighbourhood-based models for social networks: model specification issues
1. Random graph
models
Why is it important to model networks?
Approach to modelling networks
A simplified multi-layered framework
Some assumptions about proximity
Models for interactive
systems of variables
(Besag, 1974)
Exponential random graph (p*)
models
(Frank & Strauss, 1986)
Neighbourhoods depend on
proximity assumptions
Homogeneous Markov random
graphs
(Frank & Strauss, 1986)
Model specification:
edge and dyad parameters
Homogeneous Markov models
with sp =
0, for p > p0
3. New
specifications
I: the alternating
k-star hypothesis
Properties of alternating k-star models
Generalised exchange:
4-cycles in networks
(Pattison & Robins, 2002)
New specifications II. Realisation-dependent models for higher-order clustering effects
Some neighbourhoods for
4-cycle model:
independent 2-paths
More neighbourhoods for 4-cycle model
Triangle and k-triangle statistics