Vertica-cluster architecture I know that MongoDB has master-slave architecture and Cassandra has peer to peer architecture.  

I didn't find any resources about Vertica's architecture.  

Is that master slave or peer to peer?
Does Vertica cluster allow multi-read and multi-write?
There is no concept of Master in Vertica.

But there is the concept of Initiator - this node will be the node who receives the connection and will compute the query plan, divide the workload among the nodes and then gather the result sets and format the output.

As for the multi-read and multi-write. Vertica is fully ACID complaint, this articles will give you more info.
https://my.vertica.com/docs/7.0.x/HTML/Content/Authoring/ConceptsGuide/Other/Transactions.htm