The networks were evaluated by 4 distinct criteria:

1. loglik – the value of log likelihood for 10000 test samples generated by the original network,
2. size – the number of network parameters,
3. totVarDist – the direct model match computed as the Manhattan distance of the original and the learned joint probability distribution (http://en.wikipedia.org/wiki/Total_variation_distance_of_probability_measures),
4. KLdiv – the direct model match computed as the Kullback-Leibler divergence of the original and the learned joint probability distribution (http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence).

The first score shall be maximized, the other scores shall be minimized. In order to obtain the scale, your results are compared with the original network (denoted as orig) and a random network (denoted as random, its structure was learned by K2 having a random variable order with an extremely small sample size, its parameters were randomized). On top of that, there are two straightforwardly learned networks K2Random (K2 algorithm, a random order of variables, properly learned parameters) and K2correct (K2 algorithm, the correct order of variables, properly learned parameters).

I ranked your solutions in descending order, I used a weighted average of loglik, size and totVarDist. The orig network (almost necessarily) wins. At the same time, there are at least 6 proper solutions that approach the original. Other 10 solutions can be concerned as very good. The remaining models score poorly. On one hand, the cause can be a minor inattention, on the other hand, you were supposed to check before submission.

1. Do not take the ranking absolutely, the differences are small in many places. Small perturbations in criteria weighting or the sample set can result in rank changes.
2. The models with good loglik and poor totVarDist and KLdiv suffer from the variable sort that is not topological (the model occasionally works, nevertheless, the inference engine used to construct the joint probability table failed).
3. KL divergence was not employed in the final score. First, it strongly correlates with topVarDist. Second, it assigns Inf to all the models that set any of its parameters to 0. It is a reminder that priors shall always be used, but we did not deal with them explicitly in labs.