Network analyses on probabilistic graphical models

Question

I recently see examples of network analyses (such as centrality measures from network/graph theory) being applied on probabilistic graphical models (e.g. Gaussian graphical model) and there is a growing literature in psychology which continues to do the same.

(e.g. see http://journals.sagepub.com/doi/pdf/10.1177/1948550617709827)

I am reading the Machine learning textbook by Chris Bishop and I was wondering if there's a reason why most textbooks in computer science and mathematics (e.g. Bishop, Murphy, Lauritzen) tend to differentiate between graphical models and network analysis i.e. treat graphical models as multivariate statistical models and not as networks.

Is it just a matter of different perspectives between disciplines (psychology vs computer science/mathematics) or is there a (technical) reason why one should not conduct network analyses on graphical models? Thanks.

Answer 1

This is something I've been doing research into.

Network models express dependencies between observations.

Graphical models express dependencies between variables.

So, in a certain sense, they are "orthogonal" to each other (if we think about the data matrix as having variables as columns and observations as rows).

Centralities are based on reasoning from mathematical sociology, and don't relate very well to what graphical models represent.