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What are the applications of Bipartite graphs?
In a bipartite graph, vertices can be splitted into two disjoint sets so that each edge connected a vertex in one set to a vertex in the multiple set. For the AllElectronics user purchase data, one set of vertices defines users, with one users per vertex. The multiple set defines products, with one product per vertex. An edge links a user to a product, defining the purchase of the product by the user.
There are various applications of Bipartite graphs which is as follows −
Web search engines − In web search engines, search logs are archived to data user queries and the corresponding press-through data. (The press-through data tells us on which pages, given as an outcome of a search, the user pressed.)
The query and click-through data can be defined using a bipartite graph, where the two sets of vertices equivalent to queries and web pages, accordingly.
An edge connects a query to a web page if a user press the web page when asking the query. Valuable data can be acquired by cluster analyses on the query–web page bipartite graph.
For example, it can identify queries posed in several languages, but that mean the similar thing, if the press-through data for each query is same. Some web pages on the Web form a directed graph, also called the web graph, where each web page is a vertex, and each hyperlink is an edge indicating from a source page to a destination page. Cluster analysis on the web graph can acknowledge communities, discover hubs and authoritative web pages, and identify web spams.
Social network − A social network is a social structure. It can be defined as a graph, where the vertices are person or organizations, and the connection are interdependencies among the vertices, describing friendship, common interests, or collaborative activities. AllElectronics users form a social network, where each user is a vertex, and an edge connection two users if they understand each other.
As user relationship manager, it is interested in discovering useful data that can be changed from AllElectronics’ social web through cluster analysis. It can acquire clusters from the network, where users in a cluster understand each other or have friends in common.
Users within a cluster can hold one another concerning purchase decision making. Furthermore, communication medium can be created to instruct the “heads” of clusters so that promotional data can be develop out quickly.
The network is a weighted graph because an edge between two authors can produce a weight defining the strength of the collaboration including how many publications the two authors (as the end vertices) coauthored.
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