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
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