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I don't buy the index-free hype. Leaving aside the problem of a distributed implementation, imagine you have a node with lots of labeled edges going out, and you're only interested in following some of those edges. You have to find the right ones somehow - full scan of all the edges, or - an index. Or, for a more detailed comment (not mine), see eg https://www.arangodb.com/2016/04/index-free-adjacency-hybrid... .

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There are of course certain structures you can use to ease the selection of the relationships you want to follow, and Neo4j does use some of its own, breaking down relationships on a node first by type, and then by incoming or outgoing, allowing a quick selection of relevant relationships to follow depending on what's desired.

Whether additional structures are used at this level or not, the point of index-free adjacency is you do not need to utilize an index at the table/label level. The cost of performing each expansion is not dependent upon the total number of relationships or nodes in the graph, as it would be for table joins. You are only ever considering the relationships on each specific node at a time as you traverse.

Seems to me as long as you have that then you've got (table) index-free adjacency.

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