Is there a name for a component in the list of strongly-connected-components which has no outgoing edges?

For example, the single node in the lower right in the following graph.

(For example, in a Markov chain, this represents states with nonzero steady-state probabilities, although that's not the use case I'm looking for.)

  • 1
    $\begingroup$ A sink? ${}{}{}$ $\endgroup$
    – Ian
    Commented Aug 13, 2017 at 14:11
  • $\begingroup$ Not sure if there is a standard notation. Maybe minimal absorbing subgraph or minimal sink, i.e. it has zero out-degree but no proper subgraph has this propery which implies that it is strongly connected. $\endgroup$
    – M. Winter
    Commented Aug 13, 2017 at 17:15

1 Answer 1


In his book, Social and Economic Networks, Matthew Jackson refers to such component as strongly connected and closed:

A closed set of agents is a $C \subset \{1,\dots,n\}$ such that there is no directed link from an agent in $C$ to an agent outside of $C$ (that is, there is no pair $i \in C$ and $j \not\in C$ such that $T_{ij}>0$.

The terms strongly connected and closed appear together later to determine the convergence of Markov chains.


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