Bigraph

A bipartite graph is one whose vertices, V, can be divided into two independent sets, V₁ and V₂, and every edge of the graph connects one vertex in V₁ to one vertex in V₂ (Skiena 1990). If every vertex of V₁ is connected to every vertex of V₂ the graph is called a complete bipartite graph. If V₁ and V₂ have equal cardinality, meaning they have same number of vertices, the graph is called a balanced bipartite graph.

Another way to view a bipartite graph is by coloring the two vertices with different colors. Say all vertices of set V₁ will be colored green and all vertices of set V₂ will be colored red, then each edge will connect vertices of different colors.

This view helps to understand the fact that a graph that does not contain odd-length circles is a bipartite graph, because if it had an odd number of vertices, one of the edges would have endpoints of the same color.

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