**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 s _{p} =
0, for p > p_{0}**

**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**

**Change statistic for U ^{[}^{l}^{]}(x)**

**More neighbourhoods for
4-cycle model**

**Triangle and k-triangle
statistics**

**Change statistic for T ^{[}^{l}^{]}(x)**