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Mysql suitable for storing directed graph

Time:10-15

To achieve different airport flights between, we give two airports can search out all the paths. If use a mysql a side of deposit is ok for you? This will search up quite a waste of performance, or said that such a figure with a secondary database?
I now have two ideas, one is to use the mysql storage, and then write search code in the business layer.
Another is to use secondary entities to figure, but I still need to use mysql, so with two databases at the same time, this data synchronization and trouble
Do you have any good ideas, please advise
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