The graph diameter of a graph is the length graph geodesic ) between any two graph vertices graph distance .
Here length counts edges . The diameter is therefore
equal to the maximum of all values in the graph
distance matrix . The above random graphs on 10
vertices have diameters 3, 4, 5, and 7, respectively.
A disconnected graph has infinite diameter
(West 2000, p. 71).
The diameter of a graph may be computed in the Wolfram Language using GraphDiameter g ],
and a fast approximation to the diameter by GraphDiameter g ,
Method -> "PseudoDiameter" ]. Precomputed diameters for many
named graphs can be obtained using GraphData graph ,
"Diameter" ].
See also Diameter ,
Graph ,
Graph Distance ,
Graph
Distance Matrix ,
Graph Eccentricity ,
Graph Geodesic ,
Graph
Periphery ,
Graph Triameter ,
Moore
Graph ,
Oriented Diameter ,
Peripheral
Point ,
Transmission-Minimal
Regular Graph
Explore with Wolfram|Alpha
References Harary, F. Graph Theory. Skiena,
S. Implementing
Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. West, D. B. Introduction
to Graph Theory, 2nd ed. Referenced
on Wolfram|Alpha Graph Diameter
Cite this as:
Weisstein, Eric W. "Graph Diameter." From
MathWorld https://mathworld.wolfram.com/GraphDiameter.html
Subject classifications
of the "longest shortest path" (i.e.,
the longest graph geodesic) between any two graph vertices 
, where 
is a graph distance.
Here length counts edges. The diameter is therefore
equal to the maximum of all values in the graph
distance matrix. The above random graphs on 10
vertices have diameters 3, 4, 5, and 7, respectively.
