I am reading Markov Random Field Analysis. I am somewhat confused by the definition of a clique in that book.
edited: definition from the book "A clique c for $(\mathcal{S},\mathcal{N})$ is defined as a subset of sites in $\mathcal{S}$. It consists of either a single-site $c=\{i\}$, a pair of neighboring sites c=\{i,i'\}, a triple of neighboring sites c=\{i,i',i''\}, and so on.". This is the definition I am familiar with, but then the author goes on: "Note that the sites in a clique are ordered and {i,i'} is not the same clique as {i',i}, and so on."
Is this a well-known alternative definition to the typical non-ordered definition ?
What would a maximal clique be if cliques are ordered? E.g. a graph with three nodes all connected and the cliques: {1,2,3},{1,3,2},{3,2,1}... would they all be maximal cliques?
I do understand how the definition in the book may be useful for image analysis (e.g. encourage flow towards one direction so the potential has different energies depending on the order of the clique). Then again I can't see why that could not be taken into account by an alternative potential which takes all orientations into account when given a non-ordered clique.