# Doubt on d-separation

In the book: Bayesian Networks With Examples in R, the author shows three examples of d-separation:

He cites:

Then, just a few lines below, the author uses the dsep function, which returns FALSE for one of the examples previously given!!

Is this a mistake in the book? If not, what am I missing, why is his explanation so confusing?

• I think the figure just tries to show the different types of connections and is not claiming that d-separation exists in all of the examples. On the top of page 23, the authors state clearly that A and S are only d-separated if we are not conditioning on E. The figure legend should probably be worded more clearly. – COOLSerdash Jan 23 '20 at 12:50
• I agree with you, but just below 'figure 1.3' he says "some examples of d-separation covering...", so in a sense he is in fact claiming that d-separation exists in the three examples... – Chicago1988 Jan 23 '20 at 13:01

The legend is wrong (or very misleading), while the code snippet displays the correct output. In the third example, given $$E$$, the highlighted node in grey, $$A$$ and $$S$$ are not d-separated.
In this elementary configuration, $$E$$ is called a collider, and in a collider, conditioning on the common effect $$E$$ makes $$A$$ and $$S$$ dependent on each other. See for example this course p. 483.