Abstract. RPL (pronounced "ripple") is the most expressive path language for navigating in RDF graphs proposed to date that can still be evaluated with polynomial combined complexity. RPL is a lean language well-suited for integration into RDF rule languages. This integration enables a limited form of recursion for traversing RDF paths of unknown length at almost no additional cost over conjunctive triple patterns. We demonstrate the power, ease, and efficiency of RPL with two applications on top of the RPL Web interface. The demonstrator implements RPL by transformation to extended nested regular expressions (NREs). For these extended NREs we have implemented an evaluation algorithm with polynomial data complexity. To the best of our knowledge, this demo is the first implementation of NREs (or similarly expressive RDF path languages) with this complexity. MotivationWith the promise of exciting "new kinds of usage scenarios", you finally got your boss at company C to embrace linked data and connect your community forum and contact database to other online communities and FOAF profiles of your contacts. Your boss now wants to put that technology to use: "I want to cooperate with X on topic Y ! Can you get me the name of any person that works at X and that's connected to us via people that are also interested in Y (so that they have an interest in connecting us). Oh, and none of the intermediates should be our competitor Z."Though the linked data movement and related initiatives like FOAF or SIOC provide specifically for this kind of scenario, most current analysis and query tools for RDF are not up to this task: SPARQL can only compute persons connected via fixed length paths due to the lack of any form of recursion. Under an (e.g., OWL-based) entailment regime that treats foaf:knows (the FOAF property used to build social networks) as a transitive property, SPARQL can compute all connected persons, but can not ensure that all intermediate persons share the same interest. The recent extension of SPARQL with property paths (to be incorporated into SPARQL 1.1) also fails at this task, as it only allows local restrictions on the traversed edges, but not on the traversed nodes, and no repetition ( * ) over paths with restrictions on nodes and edges.