Suppose that 
is a pseudograph, 
is the edge set of 
, and 
is the family of edge sets of graph
cycles of 
.
Then 
obeys the axioms for the circuits of a matroid, and hence
is a matroid. Any matroid that can
be obtained in this way is a graphic matroid.
Graphic Matroid
See also
Matroid, PseudographThis entry contributed by Dillon Mayhew
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References
Oxley, J. G. Matroid Theory. Oxford, England: Oxford University Press, p. 11, 1991.Referenced on Wolfram|Alpha
Graphic MatroidCite this as:
Mayhew, Dillon. "Graphic Matroid." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/GraphicMatroid.html