I am using Mallet to use Conditional Random Field. From my understanding, CRF has a few kinds of markov order depending on how nodes are connected. In the figure, it's the three quarter order, the first order, and the second order from the top. 
Concept check: I'm basically confused about the terms, "markov order" and "connectivity" and "transition" because they all seem to refer to the same concept. I believe that A node can be transitioned to another node if there is an edge connecting them. Is this it or am I missing something?
The order parameters In Mallet, I can set the parameters on which markov order I want to use, and I thought it would take 1,2, 0.75... but instead it takes two parameters and they explain as "main and backoff order". What does this mean?
My task resembles a sequential tagging, which is why I tried to use CRF. The classification task I am doing highly correlates to the previous node's classification result. When I used SVM for this task, I included "Previous node label" feature and did a two-phase learning, where I first trained SVM using the truth data for "previous node label" and then trained another model using the prediction result of the first classifier. But in CRF, if I use second order, which includes previous node's label, would this kind of learning or using this feature be unnecessary? I hope I'm explaining this clearly.
