Bipartite Graphs | Understanding the Concept, Applications, and Analysis Techniques

bipartite graph

A bipartite graph is a type of graph in which the vertices can be split into two distinct groups, or partitions, such that all edges connect vertices from different partitions

A bipartite graph is a type of graph in which the vertices can be split into two distinct groups, or partitions, such that all edges connect vertices from different partitions. In other words, it is a graph in which there are no edges connecting vertices within the same partition.

Formally, let G = (V, E) be a graph, where V represents the set of vertices and E represents the set of edges. G is bipartite if the vertex set V can be partitioned into two disjoint subsets V1 and V2, such that for every edge (u, v) in E, vertex u belongs to V1 and vertex v belongs to V2 (or vice versa).

Graphically, a bipartite graph can be represented by dividing the vertices into two distinct groups and drawing edges only between vertices from different groups. It can also be represented using an adjacency matrix, where rows represent vertices from one partition and columns represent vertices from the other partition, and the entries indicate whether or not there is an edge between the corresponding vertices.

Bipartite graphs have various applications in different fields, such as computer science, biology, and social sciences. They are commonly used to model relationships between two different sets of objects, such as students and courses, customers and products, or actors and movies. Bipartite graphs can be analyzed and studied using specific algorithms and techniques tailored for this type of graph structure.

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