What Is Bipartite Graph?

A Bipartite Graph is like a fancy dating app with two groups of people: the "left swipes" and the "right swipes". The left swipes represent one set of vertices, and the right swipes represent the other set. And just like on a dating app, these two groups of people can only directly interact with each other... at least not with some fancy matching algorithm. In a bipartite graph, all the edges connect a vertex from one set to a vertex from the other set. So, if you think of the left swipes as "A-type" people and the right swipes as "B-type" people, all the edges would connect an A-type person to a B-type person. It's important to note that this differs from a regular graph, where vertices can connect to any other vertex. In a bipartite graph, the vertices are strictly divided into two sets and can only connect to vertices in the different sets. One remarkable property of bipartite graphs is that they don't contain any odd cycles. An odd cycle is a cycle with an odd number of edges, like a pentagon. In a bipartite graph, if you started at any vertex, you could only travel through edges connecting to vertices in the other set, so you couldn't end up back where you started with an odd number of edges. Bipartite graphs are used in various applications such as Job Assignment Problems, Representing a bipartite graph using a matrix, Network flow, and Project scheduling problems. Another application of Bipartite Graph is in the field of Recommender Systems, where we can use Bipartite Graph to represent users and items. Users are one set of vertices, and items are the other set of vertices. Edge represents the relationship between the user and the item. In this way, we can use Bipartite Graph to recommend items to the users based on the relationship between the users and items represented by the edges.