Let 
be a connected graph with vertex
set 
and graph distance 
. The vertex transmission, or status, of a vertex 
is
 |
(1)
|
Equivalently, if 
is the graph distance matrix of 
, then the vector of vertex transmissions is
 |
(2)
|
where 
is the all-ones vector, so vertex transmissions are the row sums of the graph distance
matrix.
The graph transmission of 
is the half-sum of all vertex transmissions,
 |
(3)
|
and is therefore identical to the Wiener index 
.
For a graph on 
vertices with mean distance 
, the average vertex transmission is 
. For connected graphs
with 
,
the usual normalized closeness centrality 
is
 |
(4)
|
