A graph is bipartite if and only if it is 2-colorable. Again A graph is bipartite if and only if every edge belongs to an odd number of bonds, minimal subsets of edges whose removal increases the number of components of the graph.
I have tried it but not understand how to implement it?
Apache AGE is a graph database that uses PostgreSQL as its backend. This means that any functionality that is not provided out-of-the-box by AGE can be implemented in PostgreSQL using custom functions. In the case of determining bipartiteness of a graph, a custom function can be written in PostgreSQL and then used within an AGE query.
You can use the python driver for apache-age to load the graph and implement a function to check if it is bipartite or not.
Check out this article for further help.
The statement you proved is not right because bipartite graph are only covered with 2 different colour that are not adjacent to each other.for e.g there are two colours red and blue red edge is connected to blue only 
Apache AGE leverages the PostgreSQL ecosystem and allows you to utilize custom functions to implement additional functionality. In the case of determining the bipartiteness of a graph, you can write a custom function in PostgreSQL and then incorporate it into your AGE queries.
You can use the following steps to determine the bipartiteness in the graph:
I would advise you to create a custom function using PostgreSQL to find bipartite-ness in a graph.
I think, as of now AGE doesn't support this feature but, you can implement it using Postgres because the AGE backend is created using PostgreSQL.
Apache AGE does not provide built-in automatic graph partioning, but you can integrate PostgreSQL which will allows you to implement various bipartitioning strategies at the PostgreSQL level.
