A mixed graph is a graph in which both directed and undirected
edges may occur.
If only directed edges exist, the graph is called a
directed graph.
If only undirected edges exist, it is called an undirected graph.
For a mixed graph with no loops or multiple edges, the Hermitian adjacency matrix represents
an undirected graph edge by 1 and an arc by the conjugate
pair 
and 
. This extends spectral questions such as perfect
state transfer to mixed graphs (Song and Lin 2026).
See also
Directed Graph,
Multigraph,
Pseudograph,
Simple Graph,
Undirected Graph,
Hermitian
Adjacency Matrix,
Perfect State Transfer
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References
Song, X. and Lin, H. "State Transfer on Mixed Graphs." Electron. J. Combin. 33, P3.60, 2026. https://doi.org/10.37236/14214.Referenced
on Wolfram|Alpha
Mixed Graph
Cite this as:
Weisstein, Eric W. "Mixed Graph." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MixedGraph.html
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