The main purpose of this talk is to explore the relationship between the 
set of conditional independence statements induced by a probability 
distribution and the set of separations induced by graphs as studied in 
graphical models. I introduce the concepts of Markov property and 
faithfulness, and provide conditions under which a given probability 
distribution is Markov or faithful to a graph in a general setting. I 
discuss the implications of these conditions in devising structural 
learning algorithms, in understanding exchangeabile vectors, and in 
random network analysis.