IOTA claims that it is not a blockchain. IOTA uses directed acylic graph (DAG) which is what ethereum ethhash is based on in its early variant (Dagger, an algorithm by Vitalik Buterin which uses directed acyclic graphs).
Can someone explain?
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A DAG is just a mathematical concept were you have directed edges and vertices, with the property that if you start from a vertice a follow the edges (in the correct direction): you cannot visit a vertice more than once.
When it comes to computer science: a DAG is a particular data-structure (understand "data-structure" as "a way to organize information") sharing the same properties as the mathematical-DAG. Usually the information is associated with vertices (but nothing prevent a developper to use a DAG with information associated to edges).
When it comes to the Tangle: a DAG-data-structure is at the heart of the system because this the data-structure in use to store transactions.
I'm not a Dagger expert, but as far as I understand, Dagger is a mining algorithm and this algorithm use a DAG internally. Dagger and it's DAG aren't use to organize transaction on the Ethereum network. So the use of the DAG-data-structure in Dagger is completely different that the usage of the DAG-data-structure in the Tangle.
Note that, strictly speaking, the main data-structure in blockchains is also a DAG (with just some additional constraints)