When are all closeness centralities zero? I have a theoretical question, but it is not homework.
The closeness centrality values of all vertices are 0 if the graph is disconnected. 
Are there other cases where the closeness centrality values of all vertices are 0?

According to Wikipedia, a node's farness is defined as the sum of its distances to all other nodes in the graph, and its closeness (or closeness centrality) is the inverse of its farness.  If the closeness centrality of a node is $0$, then its farness must be infinite, in which case it is either infinitely far from some node (i.e., the graph is disconnected), or else there are infinitely many nodes in the graph.  Either of these conditions describes the graph as a whole, so the following three conditions are equivalent:


*

*$G$ has a node with zero closeness centrality.

*Every node in $G$ has zero closeness centrality.

*$G$ is not a connected finite graph.

