A fuzzy graph is a pair 
,
where 
is a fuzzy
set on a vertex set 
and 
is a fuzzy relation on 
satisfying
 |
(1)
|
for all 
(Rosenfeld 1975). For an undirected fuzzy graph, 
is also a symmetric relation.
The support, or underlying crisp graph, has vertex set and edge set
 |  |  |
(2)
|
 |  |  |
(3)
|
When both 
and 
take values only in 
, the fuzzy graph reduces to an ordinary graph.
