Some independences rely upon context. For example, for an undirected graph $(a)-(b)-(c)$, $b$ and $c$ may be independent while $a=0$, but $b=c$ when $a=1$. Graphs will err on the side of less independence, so it would not say that $b$ and $c$ are independent and wouldn't describe the case where they were.

Context Specific Independence

Separation is used to describe which variables interact indirectly. D-Separation simply refers to separation with a directed graph.

If a path exists between two variables with only unobserved variables, then the variables are separated. Paths like this are considered active, while paths with an observed variable are considered inactive.

Michigan State University

Probabilistic models use graphs to show interactions between random variables. A graph is a set of nodes connected by vertices. A probabilistic model represents random variables with nodes and their relationships with vertices between them.

Graph Model Structure

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

Undirected Models (AKA Markov Random Fields/MRF/Markov Networks) have typical graph structure but the vertices are undirected.

Undirected Models

Separation and D-Separation

A Bayesian network or Belief Model is a probabilistic graphical model for representing knowledge about an uncertain domain where each node corresponds to a random variable and each edge represents the conditional probability for the corresponding random variables.

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