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VIVO represents data as triples.  All data is represented and stored in the form subject, predicate, object.  All entities are identified by URI.  The W3C has developed standards for RDF (Resource Description Framework) for such representations and for various serializations of RDF, including Turtle.  If you are unfamiliar with this method for data representation, see the references.  A typical VIVO for a large research institution could have well over 10 million triples.  The triples are defined using an ontology.  The ontology is described here: Ontology Reference Understanding which triples are needed for an analysis can be challenging.  The VIVO community is here to help.  Questions regarding data and data extraction using the techniques below can be posted to one of the VIVO Google Groups.  You may also wish to contact the VIVO providers at your institution who may be able to help with some of the technologies involved.

Getting Rectangles of Data

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Some applications involve getting data from multiple VIVOs.  VIVOs running version 1.10 and above provide a Triple Pattern Fragments endpoint which can be used to rapidly get all triples from a VIVO matching a triple pattern.

References

1. RDF 1.1 Primer https://www.w3.org/TR/rdf11-primer/
2. RDF 1.1 Turtle https://www.w3.org/TR/turtle/
3. Börner, Conlon, Corson-Rikert, and Ding (eds) VIVO: A Semantic Approach to Scholarly Networking and Discovery, Morgan-Claypool Publishers, 2012.  160 pages.
4. Allemang, and Hendler.  Semantic Web for the Working Ontologist, second edition.  Morgan-Kaufmann Publishers, 2011.  354 pages.
5. DuCharme. Learning SPARQL: Querying and Updating with SPARQL 1.1. O'Reilly, 2011. 235 pages.