The metric embedding distortion of an injective function 
between metric spaces
is the infimum of the constants 
for which some 
satisfies
 |
for all 
. Here, 
and 
are the respective metrics. This
normalization permits a common rescaling of all distances. A scaled isometry
has distortion 1.
Graph metrics provide finite metric spaces whose embeddings into L1 are studied with a uniform distortion bound.
