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A pseudoforest is an undirected graph in which every connected component of a graph contains at most one cycle in a graph. Thus each component is a tree or a unicyclic component. A finite tree component has one fewer edge than vertices; a finite unicyclic component has equally many edges and vertices.

A connected graph is unicyclic when it contains exactly one cycle, equivalently when its numbers of vertices and edges agree.

A pseudoforest permits both these components and acyclic tree components.