Using centrality to assess fraud

During auction sales, sellers propose objects at a minimal price and interested buyers have to outbid each other, hence making the price increase. Fraud can occur here when a seller asks fake buyers to outbid on some products, just to make the final price higher.

Have a look at the simple graph schema reproduced in the following diagram:

Users are only allowed to interact with a given sale. Let's build a simple test graph with this schema:

CREATE (U1:User {id: "U1"})
CREATE (U2:User {id: "U2"})
CREATE (U3:User {id: "U3"})
CREATE (U4:User {id: "U4"})
CREATE (U5:User {id: "U5"})

CREATE (S1:Sale {id: "S1"})
CREATE (S2:Sale {id: "S2"})
CREATE (S3:Sale {id: "S3"})

CREATE (U1)-[:INVOLVED_IN]->(S1)
CREATE (U1)-[:INVOLVED_IN]->(S2)
CREATE (U2)-[:INVOLVED_IN]->(S3)
CREATE (U3)-[:INVOLVED_IN]->(S3)
CREATE (U4)-[:INVOLVED_IN]->(S3)
CREATE (U4)-[:INVOLVED_IN]->(S2)
CREATE (U5...