Consumer behaviour
Graph theory
Graphs
Recommender systems
User interfaces
Catalogue
Conversational recommender systems
Critique graphs
Directed multigraph
Navigation
Product feature
Recommended products
User critiques
Compounds
Computer science
Data analysis
Semantics
Standards
Strongly connected components
Critique graphs were introduced as a device for analysing the behaviour of conversational recommender systems. A conversational recommender allows a user to critique a recommended product with statements such as "I'd like a similar product to this one, but cheaper". A critique graph is a directed multigraph in which the nodes represent products, and a directed edge between a pair of products represents how a user can move from one product to another by tweaking a particular product feature. It has been shown that critique graphs are not symmetric: if a user critiques a product pi and is presented with product pj, critiquing product pj in the opposite manner does not necessarily return product pi. Furthermore, it might not be possible to reach all products in a catalogue starting from a given product, or as a consequence of a particular critique some products become unreachable. This latter point is quite unsatisfactory since a user would assume that it is possible to explore the full catalogue by critiquing alone. A number of approaches to overcoming this problem have been proposed in the literature. In this paper we propose a novel approach that exploits the critique graph directly. Specifically, the unreachability is a consequence of a critique graph having more than one strongly connected component. We show how the critique graph can be modified in a minor way, thereby modifying the semantics of critiquing for a given catalogue, so that all products are always reachable.