Where to get the data for Transactions, Graphs as a Bitcoin Exchange Our team is planning to start our own Bitcoin Exchange where an end-user could Register, make transactions(Sell/Purchase bitcoin), keep their wallet and could see live Graph of all the listed crypto-currencies. And yes we do know what are all the legal, financial and technical requirements/challenges for this.

We researched about it a lot and found everytime that there are certain websites/Exchanges like blockchain.info that provide their own API for all such tasks.

However, if we want to create our own Exchange, we can't rely fully on any third party website. So, what my main question is that where do all these websites get their data from, whenever any transaction is made on their website, do they keep this record only to their selves(in their own DB) or is their any central entity of this whole blockchain web where this transaction needs to be registered also?

And where do these websites get data for their live graphs showing the current market value of all the currencies?

Any clarification of my query would be deeply appreciated.
whenever any transaction is made on their website, do they keep this record only to their selves(in their own DB) or is their any central entity of this whole blockchain web where this transaction needs to be registered also?


There is no central entity in a blockchain network. Such a thing would be antithetical to a decentralized cryptocurrency like bitcoin. A user may run a node and participate in the network, without having to trust any of it's peers to provide good information. Instead, the code validates all network interactions, providing cryptographic trust and guarantees. 

Exchange services often run as centralized databases, this allows users to initiate many transactions (buying/selling on the exchange), without incurring network transaction fees. The exchange users trade off security (trusting a third party with their coins) for this convenience. However, there are other models that exchanges can use, it is up to your imagination to find a solution that balances trust and convenience in a way that your users will want. 


  And where do these websites get data for their live graphs showing the current market value of all the currencies?


Exchanges generally define the market price of cryptocurrencies, this is not data you would pull from a third party. The market price would be discovered by users buying/selling on your exchange, if users push the price too high/low compared to other exchanges, then arbitragers will work to balance it back out.