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What are the differences between a Graph database and a Triple store? (by Matt Allen in Quora)

Graph Databases vs. RDF Triple Stores
To summarize, both graph databases and triple stores are designed to store linked data. RDF is a specific kind of linked data that is queried using SPARQL, so it is fair to say that RDF triple stores are a kind of graph database. But, there are some subtle but important differences that are described below.
How They Are Similar
·       Graph databases and rdf triple stores focus on the relationships between the data, often referred to as “linked data.” Data points are called nodes, and the relationship between one data point and another is called an edge.
·       A web of nodes and edges can be put together into interesting visualizations—a defining characteristic of graph databases.
How They Are Different
·       Graph databases are more versatile with query languages:  Neo4J can run an RDF triple store and use SPARQL but generally focuses on its own proprietary language, Cypher. Other graph databases support G, GraphLog, GOOD, SoSQL, BiQL, SNQL, and more. RDF triple stores only use SPARQL as the query language.
·       Graph databases can store various types of graphs, including undirected graphs, weighted graphs, hypergraphs, etc. RDF triple stores focus solely on storing rows of RDF triples.
·       Graph databases are node, or property, centric whereas RDF triple stores are edge-centric. RDF triple stores are really just a list of graph edges, many of which are 'properties'  of a node and not critical to the graph structure itself.
·       Graph databases are better optimized for graph traversals (degrees of separation or shortest path algorithms). With RDF triple stores, the cost of traversing an edge tends to be logarithmic.
·       RDF triple stores also provide inferences on data but graph databases do not (e.g., if humans are a subclass of mammals and man is a subclass of humans, then it can be inferred that man is a subclass of mammals).
·       RDF triple stores are more synonymous with the “semantic web” and the standardized universe of knowledge being stored as RDF triples on DBpedia and other sources whereas graph databases are seen as more pragmatic rather than academic.

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