Factors for inferencing in Bayesian Network and Markov Networks

Based on libdai implementation, I think before doing inference we need to convert the graphs into an array of factors (represented as .fg files). For example:

1) In Bayesian networks, a factor would be the D-separated distribution.

2) In Markov networks, a factor would be an element of the Gibbs distribution, or often called energy in Ising model.

Does it mean that we can write the same inference implementation for both types of networks?

If yes, what is the official algorithm that convert Bayesian networks into the array of factors? Or is there more than one way to convert it?