This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

EulerianGraphQ

 EulerianGraphQ[g] yields True if the graph g is Eulerian, and False otherwise.
• A graph is Eulerian if it has a cycle that traverses every edge exactly once.
Test whether an undirected graph is Eulerian:
Not all graphs have an Eulerian cycle:
Test whether an undirected graph is Eulerian:
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Not all graphs have an Eulerian cycle:
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 Scope   (4)
EulerianGraphQ works with undirected graphs:
Directed graphs:
EulerianGraphQ gives False for expressions which are not graphs:
Works with large graphs:
 Applications   (2)
Euler's "Seven Bridges of Köningsberg", with multiple edges removed:
Test whether the graph is Eulerian:
Label the edges visited along the Eulerian cycle:
Find an Eulerian cycle:
An Eulerian cycle can be found using FindEulerianCycle:
A connected undirected graph is Eulerian iff every graph vertex has an even degree:
A connected undirected graph is Eulerian if it can be decomposed into edge disjoint cycles:
The graphs are cycles if they are connected and have equal number of edges and vertices:
For connected directed graphs:
The line graph of an undirected Eulerian graph is Eulerian:
The line graph of an Eulerian graph is Hamiltonian:
A connected directed graph is Eulerian iff every vertex has equal in-degree and out-degree:
Cycle graphs are Eulerian:
New in 8