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Summary A graph‐realizability algorithm of a general matroid is presented in this paper. A matroid is first decomposed into maximal 3‐connected minors called atoms and the original matroid is graph‐realizable if and only if all the atoms are graph‐realizable. Each atom is reduced to a wheel or a whirl matroid by reduction and contraction operations. The graph‐realizability of an atom is tested at each step of the reconstruction process. Two examples are included to illustrate the algorithm.

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