k-linkedness in graph theory on connectivity

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What is k-linkedness in Graph theory ? It's available in Diestel but it's not very intuitive. Please explain.

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Basically, linked means that for arbitrary pairs $(s_i,t_i),i=1,...,\ell$ of vertices in $X$ there are disjoint paths $P_i$ outside $X$ which connect these pairs.

At least this is how I understand the definition in the link.


Analogy

Place $\ell$ people at arbitrary points in $X$. Give any of them a target point in $X$ which they should reach. They have to leave $X$ and can only come back in their assigned target point. Then linked $X$ means that this is possible and that the the people can walk paths which not even cross each other. And this holds for arbitrary start and end vertices.