[igraph] making sense of is_separator()

[Szabolcs Horvát]

Hello,

What is the reasoning for the following behaviours of the is_separator() function?

http://igraph.org/c/doc/igraph-Separators.html#igraph_is_separator

This makes sense to me:

graph: 1 - 2 - 3

vertex set: {2}

result: true

Removing 2 does disconnect the graph.

graph: 1 - 2 - 3

vertex set: {3}

result: false

Removing 3 doesn't.

graph: 1 - 2 - 3 - 4

vertex set: {1, 4}

result: false

Removing 1 and 4 doesn't.

graph: 1 - 2

vertex set: {}

result: false

Removing nothing does not disconnect it.

graph: 1, 2  (disconnected)

vertex set: {}

result: true

Makes sense because the graph was already disconnected

But I am puzzled by these:

graph: 1 - 2 - 3

vertex set: {1,3}

result: true

graph: 1 - 2

vertex set: {1}

result: true

Removing these does not disconnect the graph, it merely leaves a 1-node graph behind.

Why is the result then true?

Szabolcs